text:
### A Pluto.jl notebook ###
# v0.17.7

using Markdown
using InteractiveUtils

# ╔═╡ e1b18f33-19ba-4fb3-a476-47cfeb6345af
begin
	using CSV, HTTP, DataFrames, Random
	using Turing, Distributions, MCMCChains
	using MLDataUtils: rescale!
	using Plots, StatsPlots
	using StatisticalRethinking
end

# ╔═╡ eef1e512-8579-11ec-1837-0f04dc618fcb
md"""
## Bayesian inference

#### Bayes rule(theorem)

$$P(\theta|D, m) = \frac{P(D|\theta, m) P(\theta|m)}{P(D|m)}$$

-  $P(\theta|D, m)$ ` `` ` **Posterior** of $\theta$ given data D
-  $P(D|\theta, m)$ ` `` ` **Likelihood** of parameters $\theta$ in model m
-  $P(\theta|m)$ ` ` ` ` **Prior** probability of $\theta$
-  $P(D|m)$ ` `` `**Marginal likelihood** equal to $\int P(D|\theta, m)P(\theta|m)\,\mathrm{d}\theta$

###### Prediction : $P(x|D, m) = \int P(x|\theta, D, m)\,P(\theta|D, m)\, \mathrm{d}\theta$
####
##### Two simple rule
####
**Sum rule**: $$P(x) = \displaystyle\sum_{y} P(x, y)$$

**Produt rule**: $$P(x, y) = P(y|x)P(x)$$
#
Bayesian approach is very natural way of logical thinking which is flexible and permissive. Furthermore it can allow us to reflect the **uncertainty**.
Bayes rule tell us how to do inference about hypotheses(belief) from data.

Let me tell you a story

`One night you are suddenly awakened by a bright light at your window. You jumped up from bed and look out to see a large object in the sky that can only be described as saucer shaped. You are generally a skeptic and have never believed in alien, but, completely perplexed by the scene outside, you find yourself thinking, Could this be a UFO?!`

![ufo](https://c4.wallpaperflare.com/wallpaper/217/545/167/tv-show-rick-and-morty-ufo-wallpaper-preview.jpg)

`As you look toward the bright light outside, you notice more lights in the area. You also see that the large saucer-shaped object is held up by wires, and notice a camera crew. You hear a loud clap and someone call out "Cut!"`

![film](https://res.cloudinary.com/twenty20/private_images/t_standard-fit/photosp/0b6f5e3b-56be-41cd-84c4-a19a5d23134a/stock-photo-outdoor-behind-the-scenes-video-production-film-production-shooting-video-movie-film-b-roll-film-studio-set-film-industrial-0b6f5e3b-56be-41cd-84c4-a19a5d23134a.jpg)

You have, very likely, instantly changed your mind(**update your belief**) about what you think is happening in this second paragraph. Bayesian reasoning tends to be happen so quickly that you don't have any time to analyze your own thinking.

###### Learning model structure
You may wonder what is m in that bayes rule. you can consider m as so called *hyperparameter* of models. For example, when you meet clustering problems with k-means or mixture model, 'how many clusters in the data?' or 'what is the intrinsic dimensionality of the data?' in PCA. Futhermore, model selection is related to well-known *overfitting*.

###### Priors and Marginal likelihood
Priors can be subjective and there is no right prior. It can be very generous and non-informative prior like Uniform distribution or it can reflect our domain knowledge and belief into the model. For instance, there is no such thing like negative variance so that we set our prior to be lognormal or beta distribution. Prior is not the key factor of bayesian modeling, but informative prior can be useful if we set the reasonable one.

Marginal likelihood is interpreted in information field as $\log_2(\frac{1}{P(D|m)})$ , which is the number of bits of surprise at observing data D under the model m. The problem is this can be computationally intractable and often go very high dimension. That's why we use approximation methods like MCMC and Variational bayesian(inference).
These approximation methods are certainly the paramount subject to bayesian community.

"""

# ╔═╡ 3b7e0e99-5e48-4141-ac36-d855ba7aa0bf
md"""
### Let's see with a linear regression example
"""

# ╔═╡ edec49f8-576f-470a-bcae-2040a688e987
md"""
cons

    consumption of ice cream per head (in pints);
income

    average family income per week (in US Dollars);
price

    price of ice cream (per pint);
temp

    average temperature (in Fahrenheit);
"""

# ╔═╡ 9d556aef-e773-4f8d-b220-4f0de53d5c41
begin
	# Import the "Default" dataset.
	url = "https://raw.githubusercontent.com/delphinH/imagetoy/main/dataset/Icecream.csv"
	data = CSV.read(HTTP.get(url).body, DataFrame)

	# Show the first six rows of the dataset.
	first(data, 6)

end

# ╔═╡ d36eab23-6ae5-4e54-be78-8901839bbc49
describe(data)

# ╔═╡ 4f7b0614-729f-4745-9f1a-e3eb255ea7cc
size(data)

# ╔═╡ 7c307991-87d0-4a85-a3fc-26ed21ae319d
#data in matrix form
begin
	Xs = data[:, :Temp]
	ys = data[:, :Cons]
end

# ╔═╡ f57e4624-d679-4866-b95d-f0b2bc4436e0
gr()

# ╔═╡ d9e79634-8d9f-460a-bd1e-e3471dc82bcd
p=scatter(Xs, ys, color = :teal, legend=false, fmt = "png") # scatter plot of data

# ╔═╡ 9ad28f14-1545-4141-a192-6d3adc1b4f48
#define linear model with priors
@model function lin_reg(x, y)
	#priors
	α ~ Normal(mean(y), 10)
	β ~ Normal(0, 1)
	σ ~ Exponential(1)

	μ = α .+ β * (x .- mean(x))

	y ~ MvNormal(μ, σ)
end

# ╔═╡ 19954116-525f-4caa-b66d-748dd581bfaa
model = lin_reg(Xs, ys)

# ╔═╡ 22e0b5a2-663a-49eb-a4f6-fa36353186fc
chain = sample(model, NUTS(), MCMCThreads(), 1000, 2) #approximation sampling

# ╔═╡ 11c077f4-5294-4d26-98fa-a35e3e8116f1
plot(chain)

# ╔═╡ 115341f3-7d46-456f-9d7a-3ed41fbdafcd
summarystats(chain)

# ╔═╡ c6e67570-ab0b-4213-8bbf-f9b0361ba802
mean(chain[:α])

# ╔═╡ 4e8a4bef-c071-4934-91b8-aee0416e342a
begin
	Random.seed!(12)
	alpha = 0.36
	beta = 0.00347
	nid = 50
	L = Uniform(20, 80)
	L_data = rand(L, nid)
end

# ╔═╡ 23d7011f-514a-4eb5-a509-5db22e852b0e
mu = alpha .+ beta * (L_data .- mean(L_data))

# ╔═╡ a0862af8-39c9-426b-a979-3ea1af8ed579
begin
	sd = Normal(0, 0.048)
	sde = rand(sd, nid)
end

# ╔═╡ e0084ff1-0443-418d-a36a-fd67d0c61659
W_data = mu .+ sde #generate data given posterior

# ╔═╡ 16285a48-97b4-4bcf-b69a-40d4d8e3d575
begin
	#compare with observed and generated data
	scatter(Xs, ys, color = :teal, legend=false, fmt = "png")
	scatter!(L_data, W_data)
end

# ╔═╡ 5cea4149-3003-4716-8db8-fb684f8db7c4
md"""
###### Reference
Zoubin Ghahramani: MLSS 2015 Tubingen

Will Kurt: Bayesian statistics the fun way
"""

# ╔═╡ 00000000-0000-0000-0000-000000000001
PLUTO_PROJECT_TOML_CONTENTS = """
[deps]
CSV = "336ed68f-0bac-5ca0-87d4-7b16caf5d00b"
DataFrames = "a93c6f00-e57d-5684-b7b6-d8193f3e46c0"
Distributions = "31c24e10-a181-5473-b8eb-7969acd0382f"
HTTP = "cd3eb016-35fb-5094-929b-558a96fad6f3"
MCMCChains = "c7f686f2-ff18-58e9-bc7b-31028e88f75d"
MLDataUtils = "cc2ba9b6-d476-5e6d-8eaf-a92d5412d41d"
Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80"
Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
StatisticalRethinking = "2d09df54-9d0f-5258-8220-54c2a3d4fbee"
StatsPlots = "f3b207a7-027a-5e70-b257-86293d7955fd"
Turing = "fce5fe82-541a-59a6-adf8-730c64b5f9a0"

[compat]
CSV = "~0.10.2"
DataFrames = "~1.3.2"
Distributions = "~0.25.46"
HTTP = "~0.9.17"
MCMCChains = "~5.0.3"
MLDataUtils = "~0.5.4"
Plots = "~1.25.7"
StatisticalRethinking = "~4.5.0"
StatsPlots = "~0.14.31"
Turing = "~0.20.0"
"""

# ╔═╡ 00000000-0000-0000-0000-000000000002
PLUTO_MANIFEST_TOML_CONTENTS = """
# This file is machine-generated - editing it directly is not advised

[[ANSIColoredPrinters]]
git-tree-sha1 = "574baf8110975760d391c710b6341da1afa48d8c"
uuid = "a4c015fc-c6ff-483c-b24f-f7ea428134e9"
version = "0.0.1"

[[AbstractFFTs]]
deps = ["ChainRulesCore", "LinearAlgebra"]
git-tree-sha1 = "6f1d9bc1c08f9f4a8fa92e3ea3cb50153a1b40d4"
uuid = "621f4979-c628-5d54-868e-fcf4e3e8185c"
version = "1.1.0"

[[AbstractMCMC]]
deps = ["BangBang", "ConsoleProgressMonitor", "Distributed", "Logging", "LoggingExtras", "ProgressLogging", "Random", "StatsBase", "TerminalLoggers", "Transducers"]
git-tree-sha1 = "db0a7ff3fbd987055c43b4e12d2fa30aaae8749c"
uuid = "80f14c24-f653-4e6a-9b94-39d6b0f70001"
version = "3.2.1"

[[AbstractPPL]]
deps = ["AbstractMCMC", "Setfield"]
git-tree-sha1 = "fc7080c5807afd5bb95f320e1202f218a0bcc562"
uuid = "7a57a42e-76ec-4ea3-a279-07e840d6d9cf"
version = "0.3.1"

[[AbstractTrees]]
git-tree-sha1 = "03e0550477d86222521d254b741d470ba17ea0b5"
uuid = "1520ce14-60c1-5f80-bbc7-55ef81b5835c"
version = "0.3.4"

[[Adapt]]
deps = ["LinearAlgebra"]
git-tree-sha1 = "af92965fb30777147966f58acb05da51c5616b5f"
uuid = "79e6a3ab-5dfb-504d-930d-738a2a938a0e"
version = "3.3.3"

[[AdvancedHMC]]
deps = ["AbstractMCMC", "ArgCheck", "DocStringExtensions", "InplaceOps", "LinearAlgebra", "ProgressMeter", "Random", "Requires", "Setfield", "Statistics", "StatsBase", "StatsFuns", "UnPack"]
git-tree-sha1 = "189473a73d664fe2496675775b6c8a732b8dfe26"
uuid = "0bf59076-c3b1-5ca4-86bd-e02cd72cde3d"
version = "0.3.3"

[[AdvancedMH]]
deps = ["AbstractMCMC", "Distributions", "Random", "Requires"]
git-tree-sha1 = "8ad8bfddf8bb627d689ecb91599c349cbf15e971"
uuid = "5b7e9947-ddc0-4b3f-9b55-0d8042f74170"
version = "0.6.6"

[[AdvancedPS]]
deps = ["AbstractMCMC", "Distributions", "Libtask", "Random", "StatsFuns"]
git-tree-sha1 = "59c47e9525d5a807a950d8b79b5d6e60b2f6de82"
uuid = "576499cb-2369-40b2-a588-c64705576edc"
version = "0.3.3"

[[AdvancedVI]]
deps = ["Bijectors", "Distributions", "DistributionsAD", "DocStringExtensions", "ForwardDiff", "LinearAlgebra", "ProgressMeter", "Random", "Requires", "StatsBase", "StatsFuns", "Tracker"]
git-tree-sha1 = "130d6b17a3a9d420d9a6b37412cae03ffd6a64ff"
uuid = "b5ca4192-6429-45e5-a2d9-87aec30a685c"
version = "0.1.3"

[[ArgCheck]]
git-tree-sha1 = "dedbbb2ddb876f899585c4ec4433265e3017215a"
uuid = "dce04be8-c92d-5529-be00-80e4d2c0e197"
version = "2.1.0"

[[ArgTools]]
uuid = "0dad84c5-d112-42e6-8d28-ef12dabb789f"

[[Arpack]]
deps = ["Arpack_jll", "Libdl", "LinearAlgebra"]
git-tree-sha1 = "2ff92b71ba1747c5fdd541f8fc87736d82f40ec9"
uuid = "7d9fca2a-8960-54d3-9f78-7d1dccf2cb97"
version = "0.4.0"

[[Arpack_jll]]
deps = ["Libdl", "OpenBLAS_jll", "Pkg"]
git-tree-sha1 = "e214a9b9bd1b4e1b4f15b22c0994862b66af7ff7"
uuid = "68821587-b530-5797-8361-c406ea357684"
version = "3.5.0+3"

[[ArrayInterface]]
deps = ["Compat", "IfElse", "LinearAlgebra", "Requires", "SparseArrays", "Static"]
git-tree-sha1 = "1d6835607e9f214cb4210310868f8cf07eb0facc"
uuid = "4fba245c-0d91-5ea0-9b3e-6abc04ee57a9"
version = "3.1.34"

[[Artifacts]]
uuid = "56f22d72-fd6d-98f1-02f0-08ddc0907c33"

[[AxisAlgorithms]]
deps = ["LinearAlgebra", "Random", "SparseArrays", "WoodburyMatrices"]
git-tree-sha1 = "66771c8d21c8ff5e3a93379480a2307ac36863f7"
uuid = "13072b0f-2c55-5437-9ae7-d433b7a33950"
version = "1.0.1"

[[AxisArrays]]
deps = ["Dates", "IntervalSets", "IterTools", "RangeArrays"]
git-tree-sha1 = "d127d5e4d86c7680b20c35d40b503c74b9a39b5e"
uuid = "39de3d68-74b9-583c-8d2d-e117c070f3a9"
version = "0.4.4"

[[AxisKeys]]
deps = ["AbstractFFTs", "ChainRulesCore", "CovarianceEstimation", "IntervalSets", "InvertedIndices", "LazyStack", "LinearAlgebra", "NamedDims", "OffsetArrays", "Statistics", "StatsBase", "Tables"]
git-tree-sha1 = "d6ff375e8229819ef8e443b25009091e0e88eb24"
uuid = "94b1ba4f-4ee9-5380-92f1-94cde586c3c5"
version = "0.1.25"

[[BangBang]]
deps = ["Compat", "ConstructionBase", "Future", "InitialValues", "LinearAlgebra", "Requires", "Setfield", "Tables", "ZygoteRules"]
git-tree-sha1 = "d648adb5e01b77358511fb95ea2e4d384109fac9"
uuid = "198e06fe-97b7-11e9-32a5-e1d131e6ad66"
version = "0.3.35"

[[Base64]]
uuid = "2a0f44e3-6c83-55bd-87e4-b1978d98bd5f"

[[Baselet]]
git-tree-sha1 = "aebf55e6d7795e02ca500a689d326ac979aaf89e"
uuid = "9718e550-a3fa-408a-8086-8db961cd8217"
version = "0.1.1"

[[Bijectors]]
deps = ["ArgCheck", "ChainRulesCore", "Compat", "Distributions", "Functors", "IrrationalConstants", "LinearAlgebra", "LogExpFunctions", "MappedArrays", "Random", "Reexport", "Requires", "Roots", "SparseArrays", "Statistics"]
git-tree-sha1 = "369af32fcb9be65d496dc43ad0bb713705d4e859"
uuid = "76274a88-744f-5084-9051-94815aaf08c4"
version = "0.9.11"

[[BitTwiddlingConvenienceFunctions]]
deps = ["Static"]
git-tree-sha1 = "5e98d6a6aa92e5758c4d58501b7bf23732699fa3"
uuid = "62783981-4cbd-42fc-bca8-16325de8dc4b"
version = "0.1.2"

[[Bzip2_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "19a35467a82e236ff51bc17a3a44b69ef35185a2"
uuid = "6e34b625-4abd-537c-b88f-471c36dfa7a0"
version = "1.0.8+0"

[[CPUSummary]]
deps = ["Hwloc", "IfElse", "Static"]
git-tree-sha1 = "ba19d1c8ff6b9c680015033c66802dd817a9cf39"
uuid = "2a0fbf3d-bb9c-48f3-b0a9-814d99fd7ab9"
version = "0.1.7"

[[CSV]]
deps = ["CodecZlib", "Dates", "FilePathsBase", "InlineStrings", "Mmap", "Parsers", "PooledArrays", "SentinelArrays", "Tables", "Unicode", "WeakRefStrings"]
git-tree-sha1 = "9519274b50500b8029973d241d32cfbf0b127d97"
uuid = "336ed68f-0bac-5ca0-87d4-7b16caf5d00b"
version = "0.10.2"

[[Cairo_jll]]
deps = ["Artifacts", "Bzip2_jll", "Fontconfig_jll", "FreeType2_jll", "Glib_jll", "JLLWrappers", "LZO_jll", "Libdl", "Pixman_jll", "Pkg", "Xorg_libXext_jll", "Xorg_libXrender_jll", "Zlib_jll", "libpng_jll"]
git-tree-sha1 = "4b859a208b2397a7a623a03449e4636bdb17bcf2"
uuid = "83423d85-b0ee-5818-9007-b63ccbeb887a"
version = "1.16.1+1"

[[ChainRules]]
deps = ["ChainRulesCore", "Compat", "IrrationalConstants", "LinearAlgebra", "Random", "RealDot", "SparseArrays", "Statistics"]
git-tree-sha1 = "849d4cb467ea3ecbbd3efe68dacd36f9429b543c"
uuid = "082447d4-558c-5d27-93f4-14fc19e9eca2"
version = "1.26.0"

[[ChainRulesCore]]
deps = ["Compat", "LinearAlgebra", "SparseArrays"]
git-tree-sha1 = "f9982ef575e19b0e5c7a98c6e75ee496c0f73a93"
uuid = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
version = "1.12.0"

[[ChangesOfVariables]]
deps = ["ChainRulesCore", "LinearAlgebra", "Test"]
git-tree-sha1 = "bf98fa45a0a4cee295de98d4c1462be26345b9a1"
uuid = "9e997f8a-9a97-42d5-a9f1-ce6bfc15e2c0"
version = "0.1.2"

[[Clustering]]
deps = ["Distances", "LinearAlgebra", "NearestNeighbors", "Printf", "SparseArrays", "Statistics", "StatsBase"]
git-tree-sha1 = "75479b7df4167267d75294d14b58244695beb2ac"
uuid = "aaaa29a8-35af-508c-8bc3-b662a17a0fe5"
version = "0.14.2"

[[CodecZlib]]
deps = ["TranscodingStreams", "Zlib_jll"]
git-tree-sha1 = "ded953804d019afa9a3f98981d99b33e3db7b6da"
uuid = "944b1d66-785c-5afd-91f1-9de20f533193"
version = "0.7.0"

[[ColorSchemes]]
deps = ["ColorTypes", "Colors", "FixedPointNumbers", "Random"]
git-tree-sha1 = "6b6f04f93710c71550ec7e16b650c1b9a612d0b6"
uuid = "35d6a980-a343-548e-a6ea-1d62b119f2f4"
version = "3.16.0"

[[ColorTypes]]
deps = ["FixedPointNumbers", "Random"]
git-tree-sha1 = "024fe24d83e4a5bf5fc80501a314ce0d1aa35597"
uuid = "3da002f7-5984-5a60-b8a6-cbb66c0b333f"
version = "0.11.0"

[[Colors]]
deps = ["ColorTypes", "FixedPointNumbers", "Reexport"]
git-tree-sha1 = "417b0ed7b8b838aa6ca0a87aadf1bb9eb111ce40"
uuid = "5ae59095-9a9b-59fe-a467-6f913c188581"
version = "0.12.8"

[[Combinatorics]]
git-tree-sha1 = "08c8b6831dc00bfea825826be0bc8336fc369860"
uuid = "861a8166-3701-5b0c-9a16-15d98fcdc6aa"
version = "1.0.2"

[[CommonSolve]]
git-tree-sha1 = "68a0743f578349ada8bc911a5cbd5a2ef6ed6d1f"
uuid = "38540f10-b2f7-11e9-35d8-d573e4eb0ff2"
version = "0.2.0"

[[CommonSubexpressions]]
deps = ["MacroTools", "Test"]
git-tree-sha1 = "7b8a93dba8af7e3b42fecabf646260105ac373f7"
uuid = "bbf7d656-a473-5ed7-a52c-81e309532950"
version = "0.3.0"

[[Compat]]
deps = ["Base64", "Dates", "DelimitedFiles", "Distributed", "InteractiveUtils", "LibGit2", "Libdl", "LinearAlgebra", "Markdown", "Mmap", "Pkg", "Printf", "REPL", "Random", "SHA", "Serialization", "SharedArrays", "Sockets", "SparseArrays", "Statistics", "Test", "UUIDs", "Unicode"]
git-tree-sha1 = "44c37b4636bc54afac5c574d2d02b625349d6582"
uuid = "34da2185-b29b-5c13-b0c7-acf172513d20"
version = "3.41.0"

[[CompilerSupportLibraries_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "e66e0078-7015-5450-92f7-15fbd957f2ae"

[[CompositionsBase]]
git-tree-sha1 = "455419f7e328a1a2493cabc6428d79e951349769"
uuid = "a33af91c-f02d-484b-be07-31d278c5ca2b"
version = "0.1.1"

[[ConsoleProgressMonitor]]
deps = ["Logging", "ProgressMeter"]
git-tree-sha1 = "3ab7b2136722890b9af903859afcf457fa3059e8"
uuid = "88cd18e8-d9cc-4ea6-8889-5259c0d15c8b"
version = "0.1.2"

[[ConstructionBase]]
deps = ["LinearAlgebra"]
git-tree-sha1 = "f74e9d5388b8620b4cee35d4c5a618dd4dc547f4"
uuid = "187b0558-2788-49d3-abe0-74a17ed4e7c9"
version = "1.3.0"

[[Contour]]
deps = ["StaticArrays"]
git-tree-sha1 = "9f02045d934dc030edad45944ea80dbd1f0ebea7"
uuid = "d38c429a-6771-53c6-b99e-75d170b6e991"
version = "0.5.7"

[[CovarianceEstimation]]
deps = ["LinearAlgebra", "Statistics", "StatsBase"]
git-tree-sha1 = "a3e070133acab996660d31dcf479ea42849e368f"
uuid = "587fd27a-f159-11e8-2dae-1979310e6154"
version = "0.2.7"

[[Crayons]]
git-tree-sha1 = "249fe38abf76d48563e2f4556bebd215aa317e15"
uuid = "a8cc5b0e-0ffa-5ad4-8c14-923d3ee1735f"
version = "4.1.1"

[[DataAPI]]
git-tree-sha1 = "cc70b17275652eb47bc9e5f81635981f13cea5c8"
uuid = "9a962f9c-6df0-11e9-0e5d-c546b8b5ee8a"
version = "1.9.0"

[[DataFrames]]
deps = ["Compat", "DataAPI", "Future", "InvertedIndices", "IteratorInterfaceExtensions", "LinearAlgebra", "Markdown", "Missings", "PooledArrays", "PrettyTables", "Printf", "REPL", "Reexport", "SortingAlgorithms", "Statistics", "TableTraits", "Tables", "Unicode"]
git-tree-sha1 = "ae02104e835f219b8930c7664b8012c93475c340"
uuid = "a93c6f00-e57d-5684-b7b6-d8193f3e46c0"
version = "1.3.2"

[[DataStructures]]
deps = ["Compat", "InteractiveUtils", "OrderedCollections"]
git-tree-sha1 = "3daef5523dd2e769dad2365274f760ff5f282c7d"
uuid = "864edb3b-99cc-5e75-8d2d-829cb0a9cfe8"
version = "0.18.11"

[[DataValueInterfaces]]
git-tree-sha1 = "bfc1187b79289637fa0ef6d4436ebdfe6905cbd6"
uuid = "e2d170a0-9d28-54be-80f0-106bbe20a464"
version = "1.0.0"

[[DataValues]]
deps = ["DataValueInterfaces", "Dates"]
git-tree-sha1 = "d88a19299eba280a6d062e135a43f00323ae70bf"
uuid = "e7dc6d0d-1eca-5fa6-8ad6-5aecde8b7ea5"
version = "0.4.13"

[[Dates]]
deps = ["Printf"]
uuid = "ade2ca70-3891-5945-98fb-dc099432e06a"

[[DefineSingletons]]
git-tree-sha1 = "0fba8b706d0178b4dc7fd44a96a92382c9065c2c"
uuid = "244e2a9f-e319-4986-a169-4d1fe445cd52"
version = "0.1.2"

[[DelimitedFiles]]
deps = ["Mmap"]
uuid = "8bb1440f-4735-579b-a4ab-409b98df4dab"

[[DensityInterface]]
deps = ["InverseFunctions", "Test"]
git-tree-sha1 = "80c3e8639e3353e5d2912fb3a1916b8455e2494b"
uuid = "b429d917-457f-4dbc-8f4c-0cc954292b1d"
version = "0.4.0"

[[DiffResults]]
deps = ["StaticArrays"]
git-tree-sha1 = "c18e98cba888c6c25d1c3b048e4b3380ca956805"
uuid = "163ba53b-c6d8-5494-b064-1a9d43ac40c5"
version = "1.0.3"

[[DiffRules]]
deps = ["IrrationalConstants", "LogExpFunctions", "NaNMath", "Random", "SpecialFunctions"]
git-tree-sha1 = "84083a5136b6abf426174a58325ffd159dd6d94f"
uuid = "b552c78f-8df3-52c6-915a-8e097449b14b"
version = "1.9.1"

[[Distances]]
deps = ["LinearAlgebra", "SparseArrays", "Statistics", "StatsAPI"]
git-tree-sha1 = "3258d0659f812acde79e8a74b11f17ac06d0ca04"
uuid = "b4f34e82-e78d-54a5-968a-f98e89d6e8f7"
version = "0.10.7"

[[Distributed]]
deps = ["Random", "Serialization", "Sockets"]
uuid = "8ba89e20-285c-5b6f-9357-94700520ee1b"

[[Distributions]]
deps = ["ChainRulesCore", "DensityInterface", "FillArrays", "LinearAlgebra", "PDMats", "Printf", "QuadGK", "Random", "SparseArrays", "SpecialFunctions", "Statistics", "StatsBase", "StatsFuns", "Test"]
git-tree-sha1 = "2e97190dfd4382499a4ac349e8d316491c9db341"
uuid = "31c24e10-a181-5473-b8eb-7969acd0382f"
version = "0.25.46"

[[DistributionsAD]]
deps = ["Adapt", "ChainRules", "ChainRulesCore", "Compat", "DiffRules", "Distributions", "FillArrays", "LinearAlgebra", "NaNMath", "PDMats", "Random", "Requires", "SpecialFunctions", "StaticArrays", "StatsBase", "StatsFuns", "ZygoteRules"]
git-tree-sha1 = "61805bf57113a52435a13ca0bb588daf8848784d"
uuid = "ced4e74d-a319-5a8a-b0ac-84af2272839c"
version = "0.6.37"

[[DocStringExtensions]]
deps = ["LibGit2"]
git-tree-sha1 = "b19534d1895d702889b219c382a6e18010797f0b"
uuid = "ffbed154-4ef7-542d-bbb7-c09d3a79fcae"
version = "0.8.6"

[[Documenter]]
deps = ["ANSIColoredPrinters", "Base64", "Dates", "DocStringExtensions", "IOCapture", "InteractiveUtils", "JSON", "LibGit2", "Logging", "Markdown", "REPL", "Test", "Unicode"]
git-tree-sha1 = "75c6cf9d99e0efc79b724f5566726ad3ad010a01"
uuid = "e30172f5-a6a5-5a46-863b-614d45cd2de4"
version = "0.27.12"

[[Downloads]]
deps = ["ArgTools", "LibCURL", "NetworkOptions"]
uuid = "f43a241f-c20a-4ad4-852c-f6b1247861c6"

[[DynamicPPL]]
deps = ["AbstractMCMC", "AbstractPPL", "BangBang", "Bijectors", "ChainRulesCore", "Distributions", "LinearAlgebra", "MacroTools", "Random", "Setfield", "Test", "ZygoteRules"]
git-tree-sha1 = "807d28d2cf888ca1bd8aa4786fd19fcbb2f6ad7d"
uuid = "366bfd00-2699-11ea-058f-f148b4cae6d8"
version = "0.17.3"

[[EarCut_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "3f3a2501fa7236e9b911e0f7a588c657e822bb6d"
uuid = "5ae413db-bbd1-5e63-b57d-d24a61df00f5"
version = "2.2.3+0"

[[EllipsisNotation]]
deps = ["ArrayInterface"]
git-tree-sha1 = "9aad812fb7c4c038da7cab5a069f502e6e3ae030"
uuid = "da5c29d0-fa7d-589e-88eb-ea29b0a81949"
version = "1.1.1"

[[EllipticalSliceSampling]]
deps = ["AbstractMCMC", "ArrayInterface", "Distributions", "Random", "Statistics"]
git-tree-sha1 = "c25a7254cf745720ddf9051cd0d2792b3baaca0e"
uuid = "cad2338a-1db2-11e9-3401-43bc07c9ede2"
version = "0.4.6"

[[Expat_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "ae13fcbc7ab8f16b0856729b050ef0c446aa3492"
uuid = "2e619515-83b5-522b-bb60-26c02a35a201"
version = "2.4.4+0"

[[FFMPEG]]
deps = ["FFMPEG_jll"]
git-tree-sha1 = "b57e3acbe22f8484b4b5ff66a7499717fe1a9cc8"
uuid = "c87230d0-a227-11e9-1b43-d7ebe4e7570a"
version = "0.4.1"

[[FFMPEG_jll]]
deps = ["Artifacts", "Bzip2_jll", "FreeType2_jll", "FriBidi_jll", "JLLWrappers", "LAME_jll", "Libdl", "Ogg_jll", "OpenSSL_jll", "Opus_jll", "Pkg", "Zlib_jll", "libass_jll", "libfdk_aac_jll", "libvorbis_jll", "x264_jll", "x265_jll"]
git-tree-sha1 = "d8a578692e3077ac998b50c0217dfd67f21d1e5f"
uuid = "b22a6f82-2f65-5046-a5b2-351ab43fb4e5"
version = "4.4.0+0"

[[FFTW]]
deps = ["AbstractFFTs", "FFTW_jll", "LinearAlgebra", "MKL_jll", "Preferences", "Reexport"]
git-tree-sha1 = "463cb335fa22c4ebacfd1faba5fde14edb80d96c"
uuid = "7a1cc6ca-52ef-59f5-83cd-3a7055c09341"
version = "1.4.5"

[[FFTW_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "c6033cc3892d0ef5bb9cd29b7f2f0331ea5184ea"
uuid = "f5851436-0d7a-5f13-b9de-f02708fd171a"
version = "3.3.10+0"

[[FilePathsBase]]
deps = ["Compat", "Dates", "Mmap", "Printf", "Test", "UUIDs"]
git-tree-sha1 = "04d13bfa8ef11720c24e4d840c0033d145537df7"
uuid = "48062228-2e41-5def-b9a4-89aafe57970f"
version = "0.9.17"

[[FillArrays]]
deps = ["LinearAlgebra", "Random", "SparseArrays", "Statistics"]
git-tree-sha1 = "8756f9935b7ccc9064c6eef0bff0ad643df733a3"
uuid = "1a297f60-69ca-5386-bcde-b61e274b549b"
version = "0.12.7"

[[FiniteDiff]]
deps = ["ArrayInterface", "LinearAlgebra", "Requires", "SparseArrays", "StaticArrays"]
git-tree-sha1 = "6eae72e9943d8992d14359c32aed5f892bda1569"
uuid = "6a86dc24-6348-571c-b903-95158fe2bd41"
version = "2.10.0"

[[FixedPointNumbers]]
deps = ["Statistics"]
git-tree-sha1 = "335bfdceacc84c5cdf16aadc768aa5ddfc5383cc"
uuid = "53c48c17-4a7d-5ca2-90c5-79b7896eea93"
version = "0.8.4"

[[Fontconfig_jll]]
deps = ["Artifacts", "Bzip2_jll", "Expat_jll", "FreeType2_jll", "JLLWrappers", "Libdl", "Libuuid_jll", "Pkg", "Zlib_jll"]
git-tree-sha1 = "21efd19106a55620a188615da6d3d06cd7f6ee03"
uuid = "a3f928ae-7b40-5064-980b-68af3947d34b"
version = "2.13.93+0"

[[Formatting]]
deps = ["Printf"]
git-tree-sha1 = "8339d61043228fdd3eb658d86c926cb282ae72a8"
uuid = "59287772-0a20-5a39-b81b-1366585eb4c0"
version = "0.4.2"

[[ForwardDiff]]
deps = ["CommonSubexpressions", "DiffResults", "DiffRules", "LinearAlgebra", "LogExpFunctions", "NaNMath", "Preferences", "Printf", "Random", "SpecialFunctions", "StaticArrays"]
git-tree-sha1 = "1bd6fc0c344fc0cbee1f42f8d2e7ec8253dda2d2"
uuid = "f6369f11-7733-5829-9624-2563aa707210"
version = "0.10.25"

[[FreeType2_jll]]
deps = ["Artifacts", "Bzip2_jll", "JLLWrappers", "Libdl", "Pkg", "Zlib_jll"]
git-tree-sha1 = "87eb71354d8ec1a96d4a7636bd57a7347dde3ef9"
uuid = "d7e528f0-a631-5988-bf34-fe36492bcfd7"
version = "2.10.4+0"

[[FriBidi_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "aa31987c2ba8704e23c6c8ba8a4f769d5d7e4f91"
uuid = "559328eb-81f9-559d-9380-de523a88c83c"
version = "1.0.10+0"

[[Functors]]
git-tree-sha1 = "e4768c3b7f597d5a352afa09874d16e3c3f6ead2"
uuid = "d9f16b24-f501-4c13-a1f2-28368ffc5196"
version = "0.2.7"

[[Future]]
deps = ["Random"]
uuid = "9fa8497b-333b-5362-9e8d-4d0656e87820"

[[GLFW_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Libglvnd_jll", "Pkg", "Xorg_libXcursor_jll", "Xorg_libXi_jll", "Xorg_libXinerama_jll", "Xorg_libXrandr_jll"]
git-tree-sha1 = "51d2dfe8e590fbd74e7a842cf6d13d8a2f45dc01"
uuid = "0656b61e-2033-5cc2-a64a-77c0f6c09b89"
version = "3.3.6+0"

[[GR]]
deps = ["Base64", "DelimitedFiles", "GR_jll", "HTTP", "JSON", "Libdl", "LinearAlgebra", "Pkg", "Printf", "Random", "RelocatableFolders", "Serialization", "Sockets", "Test", "UUIDs"]
git-tree-sha1 = "4a740db447aae0fbeb3ee730de1afbb14ac798a1"
uuid = "28b8d3ca-fb5f-59d9-8090-bfdbd6d07a71"
version = "0.63.1"

[[GR_jll]]
deps = ["Artifacts", "Bzip2_jll", "Cairo_jll", "FFMPEG_jll", "Fontconfig_jll", "GLFW_jll", "JLLWrappers", "JpegTurbo_jll", "Libdl", "Libtiff_jll", "Pixman_jll", "Pkg", "Qt5Base_jll", "Zlib_jll", "libpng_jll"]
git-tree-sha1 = "aa22e1ee9e722f1da183eb33370df4c1aeb6c2cd"
uuid = "d2c73de3-f751-5644-a686-071e5b155ba9"
version = "0.63.1+0"

[[GeometryBasics]]
deps = ["EarCut_jll", "IterTools", "LinearAlgebra", "StaticArrays", "StructArrays", "Tables"]
git-tree-sha1 = "58bcdf5ebc057b085e58d95c138725628dd7453c"
uuid = "5c1252a2-5f33-56bf-86c9-59e7332b4326"
version = "0.4.1"

[[Gettext_jll]]
deps = ["Artifacts", "CompilerSupportLibraries_jll", "JLLWrappers", "Libdl", "Libiconv_jll", "Pkg", "XML2_jll"]
git-tree-sha1 = "9b02998aba7bf074d14de89f9d37ca24a1a0b046"
uuid = "78b55507-aeef-58d4-861c-77aaff3498b1"
version = "0.21.0+0"

[[Glib_jll]]
deps = ["Artifacts", "Gettext_jll", "JLLWrappers", "Libdl", "Libffi_jll", "Libiconv_jll", "Libmount_jll", "PCRE_jll", "Pkg", "Zlib_jll"]
git-tree-sha1 = "a32d672ac2c967f3deb8a81d828afc739c838a06"
uuid = "7746bdde-850d-59dc-9ae8-88ece973131d"
version = "2.68.3+2"

[[Graphite2_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "344bf40dcab1073aca04aa0df4fb092f920e4011"
uuid = "3b182d85-2403-5c21-9c21-1e1f0cc25472"
version = "1.3.14+0"

[[Grisu]]
git-tree-sha1 = "53bb909d1151e57e2484c3d1b53e19552b887fb2"
uuid = "42e2da0e-8278-4e71-bc24-59509adca0fe"
version = "1.0.2"

[[HTTP]]
deps = ["Base64", "Dates", "IniFile", "Logging", "MbedTLS", "NetworkOptions", "Sockets", "URIs"]
git-tree-sha1 = "0fa77022fe4b511826b39c894c90daf5fce3334a"
uuid = "cd3eb016-35fb-5094-929b-558a96fad6f3"
version = "0.9.17"

[[HarfBuzz_jll]]
deps = ["Artifacts", "Cairo_jll", "Fontconfig_jll", "FreeType2_jll", "Glib_jll", "Graphite2_jll", "JLLWrappers", "Libdl", "Libffi_jll", "Pkg"]
git-tree-sha1 = "129acf094d168394e80ee1dc4bc06ec835e510a3"
uuid = "2e76f6c2-a576-52d4-95c1-20adfe4de566"
version = "2.8.1+1"

[[HostCPUFeatures]]
deps = ["BitTwiddlingConvenienceFunctions", "IfElse", "Libdl", "Static"]
git-tree-sha1 = "3965a3216446a6b020f0d48f1ba94ef9ec01720d"
uuid = "3e5b6fbb-0976-4d2c-9146-d79de83f2fb0"
version = "0.1.6"

[[Hwloc]]
deps = ["Hwloc_jll"]
git-tree-sha1 = "92d99146066c5c6888d5a3abc871e6a214388b91"
uuid = "0e44f5e4-bd66-52a0-8798-143a42290a1d"
version = "2.0.0"

[[Hwloc_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "d8bccde6fc8300703673ef9e1383b11403ac1313"
uuid = "e33a78d0-f292-5ffc-b300-72abe9b543c8"
version = "2.7.0+0"

[[IOCapture]]
deps = ["Logging", "Random"]
git-tree-sha1 = "f7be53659ab06ddc986428d3a9dcc95f6fa6705a"
uuid = "b5f81e59-6552-4d32-b1f0-c071b021bf89"
version = "0.2.2"

[[IRTools]]
deps = ["InteractiveUtils", "MacroTools", "Test"]
git-tree-sha1 = "006127162a51f0effbdfaab5ac0c83f8eb7ea8f3"
uuid = "7869d1d1-7146-5819-86e3-90919afe41df"
version = "0.4.4"

[[IfElse]]
git-tree-sha1 = "debdd00ffef04665ccbb3e150747a77560e8fad1"
uuid = "615f187c-cbe4-4ef1-ba3b-2fcf58d6d173"
version = "0.1.1"

[[IniFile]]
deps = ["Test"]
git-tree-sha1 = "098e4d2c533924c921f9f9847274f2ad89e018b8"
uuid = "83e8ac13-25f8-5344-8a64-a9f2b223428f"
version = "0.5.0"

[[InitialValues]]
git-tree-sha1 = "4da0f88e9a39111c2fa3add390ab15f3a44f3ca3"
uuid = "22cec73e-a1b8-11e9-2c92-598750a2cf9c"
version = "0.3.1"

[[InlineStrings]]
deps = ["Parsers"]
git-tree-sha1 = "61feba885fac3a407465726d0c330b3055df897f"
uuid = "842dd82b-1e85-43dc-bf29-5d0ee9dffc48"
version = "1.1.2"

[[InplaceOps]]
deps = ["LinearAlgebra", "Test"]
git-tree-sha1 = "50b41d59e7164ab6fda65e71049fee9d890731ff"
uuid = "505f98c9-085e-5b2c-8e89-488be7bf1f34"
version = "0.3.0"

[[IntelOpenMP_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "d979e54b71da82f3a65b62553da4fc3d18c9004c"
uuid = "1d5cc7b8-4909-519e-a0f8-d0f5ad9712d0"
version = "2018.0.3+2"

[[InteractiveUtils]]
deps = ["Markdown"]
uuid = "b77e0a4c-d291-57a0-90e8-8db25a27a240"

[[Interpolations]]
deps = ["AxisAlgorithms", "ChainRulesCore", "LinearAlgebra", "OffsetArrays", "Random", "Ratios", "Requires", "SharedArrays", "SparseArrays", "StaticArrays", "WoodburyMatrices"]
git-tree-sha1 = "b15fc0a95c564ca2e0a7ae12c1f095ca848ceb31"
uuid = "a98d9a8b-a2ab-59e6-89dd-64a1c18fca59"
version = "0.13.5"

[[IntervalSets]]
deps = ["Dates", "EllipsisNotation", "Statistics"]
git-tree-sha1 = "3cc368af3f110a767ac786560045dceddfc16758"
uuid = "8197267c-284f-5f27-9208-e0e47529a953"
version = "0.5.3"

[[InverseFunctions]]
deps = ["Test"]
git-tree-sha1 = "a7254c0acd8e62f1ac75ad24d5db43f5f19f3c65"
uuid = "3587e190-3f89-42d0-90ee-14403ec27112"
version = "0.1.2"

[[InvertedIndices]]
git-tree-sha1 = "bee5f1ef5bf65df56bdd2e40447590b272a5471f"
uuid = "41ab1584-1d38-5bbf-9106-f11c6c58b48f"
version = "1.1.0"

[[IrrationalConstants]]
git-tree-sha1 = "7fd44fd4ff43fc60815f8e764c0f352b83c49151"
uuid = "92d709cd-6900-40b7-9082-c6be49f344b6"
version = "0.1.1"

[[IterTools]]
git-tree-sha1 = "fa6287a4469f5e048d763df38279ee729fbd44e5"
uuid = "c8e1da08-722c-5040-9ed9-7db0dc04731e"
version = "1.4.0"

[[IteratorInterfaceExtensions]]
git-tree-sha1 = "a3f24677c21f5bbe9d2a714f95dcd58337fb2856"
uuid = "82899510-4779-5014-852e-03e436cf321d"
version = "1.0.0"

[[JLLWrappers]]
deps = ["Preferences"]
git-tree-sha1 = "abc9885a7ca2052a736a600f7fa66209f96506e1"
uuid = "692b3bcd-3c85-4b1f-b108-f13ce0eb3210"
version = "1.4.1"

[[JSON]]
deps = ["Dates", "Mmap", "Parsers", "Unicode"]
git-tree-sha1 = "8076680b162ada2a031f707ac7b4953e30667a37"
uuid = "682c06a0-de6a-54ab-a142-c8b1cf79cde6"
version = "0.21.2"

[[JpegTurbo_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "d735490ac75c5cb9f1b00d8b5509c11984dc6943"
uuid = "aacddb02-875f-59d6-b918-886e6ef4fbf8"
version = "2.1.0+0"

[[KernelDensity]]
deps = ["Distributions", "DocStringExtensions", "FFTW", "Interpolations", "StatsBase"]
git-tree-sha1 = "591e8dc09ad18386189610acafb970032c519707"
uuid = "5ab0869b-81aa-558d-bb23-cbf5423bbe9b"
version = "0.6.3"

[[LAME_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "f6250b16881adf048549549fba48b1161acdac8c"
uuid = "c1c5ebd0-6772-5130-a774-d5fcae4a789d"
version = "3.100.1+0"

[[LRUCache]]
git-tree-sha1 = "d64a0aff6691612ab9fb0117b0995270871c5dfc"
uuid = "8ac3fa9e-de4c-5943-b1dc-09c6b5f20637"
version = "1.3.0"

[[LZO_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "e5b909bcf985c5e2605737d2ce278ed791b89be6"
uuid = "dd4b983a-f0e5-5f8d-a1b7-129d4a5fb1ac"
version = "2.10.1+0"

[[LaTeXStrings]]
git-tree-sha1 = "f2355693d6778a178ade15952b7ac47a4ff97996"
uuid = "b964fa9f-0449-5b57-a5c2-d3ea65f4040f"
version = "1.3.0"

[[Latexify]]
deps = ["Formatting", "InteractiveUtils", "LaTeXStrings", "MacroTools", "Markdown", "Printf", "Requires"]
git-tree-sha1 = "a8f4f279b6fa3c3c4f1adadd78a621b13a506bce"
uuid = "23fbe1c1-3f47-55db-b15f-69d7ec21a316"
version = "0.15.9"

[[LayoutPointers]]
deps = ["ArrayInterface", "LinearAlgebra", "ManualMemory", "SIMDTypes", "Static"]
git-tree-sha1 = "6dd77ee76188b0365f7d882d674b95796076fa2c"
uuid = "10f19ff3-798f-405d-979b-55457f8fc047"
version = "0.1.5"

[[LazyArtifacts]]
deps = ["Artifacts", "Pkg"]
uuid = "4af54fe1-eca0-43a8-85a7-787d91b784e3"

[[LazyStack]]
deps = ["LinearAlgebra", "NamedDims", "OffsetArrays", "Test", "ZygoteRules"]
git-tree-sha1 = "a8bf67afad3f1ee59d367267adb7c44ccac7fdee"
uuid = "1fad7336-0346-5a1a-a56f-a06ba010965b"
version = "0.0.7"

[[LearnBase]]
deps = ["LinearAlgebra", "StatsBase"]
git-tree-sha1 = "47e6f4623c1db88570c7a7fa66c6528b92ba4725"
uuid = "7f8f8fb0-2700-5f03-b4bd-41f8cfc144b6"
version = "0.3.0"

[[LeftChildRightSiblingTrees]]
deps = ["AbstractTrees"]
git-tree-sha1 = "b864cb409e8e445688bc478ef87c0afe4f6d1f8d"
uuid = "1d6d02ad-be62-4b6b-8a6d-2f90e265016e"
version = "0.1.3"

[[LibCURL]]
deps = ["LibCURL_jll", "MozillaCACerts_jll"]
uuid = "b27032c2-a3e7-50c8-80cd-2d36dbcbfd21"

[[LibCURL_jll]]
deps = ["Artifacts", "LibSSH2_jll", "Libdl", "MbedTLS_jll", "Zlib_jll", "nghttp2_jll"]
uuid = "deac9b47-8bc7-5906-a0fe-35ac56dc84c0"

[[LibGit2]]
deps = ["Base64", "NetworkOptions", "Printf", "SHA"]
uuid = "76f85450-5226-5b5a-8eaa-529ad045b433"

[[LibSSH2_jll]]
deps = ["Artifacts", "Libdl", "MbedTLS_jll"]
uuid = "29816b5a-b9ab-546f-933c-edad1886dfa8"

[[Libdl]]
uuid = "8f399da3-3557-5675-b5ff-fb832c97cbdb"

[[Libffi_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "0b4a5d71f3e5200a7dff793393e09dfc2d874290"
uuid = "e9f186c6-92d2-5b65-8a66-fee21dc1b490"
version = "3.2.2+1"

[[Libgcrypt_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Libgpg_error_jll", "Pkg"]
git-tree-sha1 = "64613c82a59c120435c067c2b809fc61cf5166ae"
uuid = "d4300ac3-e22c-5743-9152-c294e39db1e4"
version = "1.8.7+0"

[[Libglvnd_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll", "Xorg_libXext_jll"]
git-tree-sha1 = "7739f837d6447403596a75d19ed01fd08d6f56bf"
uuid = "7e76a0d4-f3c7-5321-8279-8d96eeed0f29"
version = "1.3.0+3"

[[Libgpg_error_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "c333716e46366857753e273ce6a69ee0945a6db9"
uuid = "7add5ba3-2f88-524e-9cd5-f83b8a55f7b8"
version = "1.42.0+0"

[[Libiconv_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "42b62845d70a619f063a7da093d995ec8e15e778"
uuid = "94ce4f54-9a6c-5748-9c1c-f9c7231a4531"
version = "1.16.1+1"

[[Libmount_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "9c30530bf0effd46e15e0fdcf2b8636e78cbbd73"
uuid = "4b2f31a3-9ecc-558c-b454-b3730dcb73e9"
version = "2.35.0+0"

[[Libtask]]
deps = ["IRTools", "LRUCache", "LinearAlgebra", "MacroTools", "Statistics"]
git-tree-sha1 = "b82a20181e1786ef10a6f2b1309db8b27b330aaa"
uuid = "6f1fad26-d15e-5dc8-ae53-837a1d7b8c9f"
version = "0.6.6"

[[Libtiff_jll]]
deps = ["Artifacts", "JLLWrappers", "JpegTurbo_jll", "Libdl", "Pkg", "Zlib_jll", "Zstd_jll"]
git-tree-sha1 = "340e257aada13f95f98ee352d316c3bed37c8ab9"
uuid = "89763e89-9b03-5906-acba-b20f662cd828"
version = "4.3.0+0"

[[Libuuid_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "7f3efec06033682db852f8b3bc3c1d2b0a0ab066"
uuid = "38a345b3-de98-5d2b-a5d3-14cd9215e700"
version = "2.36.0+0"

[[LineSearches]]
deps = ["LinearAlgebra", "NLSolversBase", "NaNMath", "Parameters", "Printf"]
git-tree-sha1 = "f27132e551e959b3667d8c93eae90973225032dd"
uuid = "d3d80556-e9d4-5f37-9878-2ab0fcc64255"
version = "7.1.1"

[[LinearAlgebra]]
deps = ["Libdl"]
uuid = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"

[[LogExpFunctions]]
deps = ["ChainRulesCore", "ChangesOfVariables", "DocStringExtensions", "InverseFunctions", "IrrationalConstants", "LinearAlgebra"]
git-tree-sha1 = "e5718a00af0ab9756305a0392832c8952c7426c1"
uuid = "2ab3a3ac-af41-5b50-aa03-7779005ae688"
version = "0.3.6"

[[Logging]]
uuid = "56ddb016-857b-54e1-b83d-db4d58db5568"

[[LoggingExtras]]
deps = ["Dates", "Logging"]
git-tree-sha1 = "dfeda1c1130990428720de0024d4516b1902ce98"
uuid = "e6f89c97-d47a-5376-807f-9c37f3926c36"
version = "0.4.7"

[[MCMCChains]]
deps = ["AbstractMCMC", "AxisArrays", "Compat", "Dates", "Distributions", "Formatting", "IteratorInterfaceExtensions", "KernelDensity", "LinearAlgebra", "MCMCDiagnosticTools", "MLJModelInterface", "NaturalSort", "OrderedCollections", "PrettyTables", "Random", "RecipesBase", "Serialization", "Statistics", "StatsBase", "StatsFuns", "TableTraits", "Tables"]
git-tree-sha1 = "ddafbd2a95114d13721f2b6ddeeaee9529d6bc2b"
uuid = "c7f686f2-ff18-58e9-bc7b-31028e88f75d"
version = "5.0.3"

[[MCMCDiagnosticTools]]
deps = ["AbstractFFTs", "DataAPI", "Distributions", "LinearAlgebra", "MLJModelInterface", "Random", "SpecialFunctions", "Statistics", "StatsBase", "Tables"]
git-tree-sha1 = "058d08594e91ba1d98dcc3669f9421a76824aa95"
uuid = "be115224-59cd-429b-ad48-344e309966f0"
version = "0.1.3"

[[MKL_jll]]
deps = ["Artifacts", "IntelOpenMP_jll", "JLLWrappers", "LazyArtifacts", "Libdl", "Pkg"]
git-tree-sha1 = "5455aef09b40e5020e1520f551fa3135040d4ed0"
uuid = "856f044c-d86e-5d09-b602-aeab76dc8ba7"
version = "2021.1.1+2"

[[MLDataPattern]]
deps = ["LearnBase", "MLLabelUtils", "Random", "SparseArrays", "StatsBase"]
git-tree-sha1 = "e99514e96e8b8129bb333c69e063a56ab6402b5b"
uuid = "9920b226-0b2a-5f5f-9153-9aa70a013f8b"
version = "0.5.4"

[[MLDataUtils]]
deps = ["DataFrames", "DelimitedFiles", "LearnBase", "MLDataPattern", "MLLabelUtils", "Statistics", "StatsBase"]
git-tree-sha1 = "ee54803aea12b9c8ee972e78ece11ac6023715e6"
uuid = "cc2ba9b6-d476-5e6d-8eaf-a92d5412d41d"
version = "0.5.4"

[[MLJModelInterface]]
deps = ["Random", "ScientificTypesBase", "StatisticalTraits"]
git-tree-sha1 = "8da86dcf5a9ea48413c7e920a990f0ea1869f9cb"
uuid = "e80e1ace-859a-464e-9ed9-23947d8ae3ea"
version = "1.3.6"

[[MLLabelUtils]]
deps = ["LearnBase", "MappedArrays", "StatsBase"]
git-tree-sha1 = "fd75d4b0c4016e047bbb6263eecf7ae3891af522"
uuid = "66a33bbf-0c2b-5fc8-a008-9da813334f0a"
version = "0.5.7"

[[MacroTools]]
deps = ["Markdown", "Random"]
git-tree-sha1 = "3d3e902b31198a27340d0bf00d6ac452866021cf"
uuid = "1914dd2f-81c6-5fcd-8719-6d5c9610ff09"
version = "0.5.9"

[[ManualMemory]]
git-tree-sha1 = "96cc3585aaadd885960141952276c54ca3910543"
uuid = "d125e4d3-2237-4719-b19c-fa641b8a4667"
version = "0.1.7"

[[MappedArrays]]
git-tree-sha1 = "e8b359ef06ec72e8c030463fe02efe5527ee5142"
uuid = "dbb5928d-eab1-5f90-85c2-b9b0edb7c900"
version = "0.4.1"

[[Markdown]]
deps = ["Base64"]
uuid = "d6f4376e-aef5-505a-96c1-9c027394607a"

[[MbedTLS]]
deps = ["Dates", "MbedTLS_jll", "Random", "Sockets"]
git-tree-sha1 = "1c38e51c3d08ef2278062ebceade0e46cefc96fe"
uuid = "739be429-bea8-5141-9913-cc70e7f3736d"
version = "1.0.3"

[[MbedTLS_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "c8ffd9c3-330d-5841-b78e-0817d7145fa1"

[[Measures]]
git-tree-sha1 = "e498ddeee6f9fdb4551ce855a46f54dbd900245f"
uuid = "442fdcdd-2543-5da2-b0f3-8c86c306513e"
version = "0.3.1"

[[MicroCollections]]
deps = ["BangBang", "InitialValues", "Setfield"]
git-tree-sha1 = "6bb7786e4f24d44b4e29df03c69add1b63d88f01"
uuid = "128add7d-3638-4c79-886c-908ea0c25c34"
version = "0.1.2"

[[Missings]]
deps = ["DataAPI"]
git-tree-sha1 = "bf210ce90b6c9eed32d25dbcae1ebc565df2687f"
uuid = "e1d29d7a-bbdc-5cf2-9ac0-f12de2c33e28"
version = "1.0.2"

[[Mmap]]
uuid = "a63ad114-7e13-5084-954f-fe012c677804"

[[MonteCarloMeasurements]]
deps = ["Distributed", "Distributions", "LinearAlgebra", "MacroTools", "Random", "RecipesBase", "Requires", "SLEEFPirates", "StaticArrays", "Statistics", "StatsBase", "Test"]
git-tree-sha1 = "a438746036111a49ba2cb435681aeef0f1d8e9bc"
uuid = "0987c9cc-fe09-11e8-30f0-b96dd679fdca"
version = "1.0.6"

[[MozillaCACerts_jll]]
uuid = "14a3606d-f60d-562e-9121-12d972cd8159"

[[MultivariateStats]]
deps = ["Arpack", "LinearAlgebra", "SparseArrays", "Statistics", "StatsBase"]
git-tree-sha1 = "8d958ff1854b166003238fe191ec34b9d592860a"
uuid = "6f286f6a-111f-5878-ab1e-185364afe411"
version = "0.8.0"

[[NLSolversBase]]
deps = ["DiffResults", "Distributed", "FiniteDiff", "ForwardDiff"]
git-tree-sha1 = "50310f934e55e5ca3912fb941dec199b49ca9b68"
uuid = "d41bc354-129a-5804-8e4c-c37616107c6c"
version = "7.8.2"

[[NNlib]]
deps = ["Adapt", "ChainRulesCore", "Compat", "LinearAlgebra", "Pkg", "Requires", "Statistics"]
git-tree-sha1 = "0b9f48ee4a793ae1d2c766093e9f45f405de6231"
uuid = "872c559c-99b0-510c-b3b7-b6c96a88d5cd"
version = "0.8.0"

[[NaNMath]]
git-tree-sha1 = "b086b7ea07f8e38cf122f5016af580881ac914fe"
uuid = "77ba4419-2d1f-58cd-9bb1-8ffee604a2e3"
version = "0.3.7"

[[NamedArrays]]
deps = ["Combinatorics", "DataStructures", "DelimitedFiles", "InvertedIndices", "LinearAlgebra", "Random", "Requires", "SparseArrays", "Statistics"]
git-tree-sha1 = "2fd5787125d1a93fbe30961bd841707b8a80d75b"
uuid = "86f7a689-2022-50b4-a561-43c23ac3c673"
version = "0.9.6"

[[NamedDims]]
deps = ["AbstractFFTs", "ChainRulesCore", "CovarianceEstimation", "LinearAlgebra", "Pkg", "Requires", "Statistics"]
git-tree-sha1 = "af6febbfede908c04e19bed954350ac687d892b2"
uuid = "356022a1-0364-5f58-8944-0da4b18d706f"
version = "0.2.45"

[[NamedTupleTools]]
git-tree-sha1 = "63831dcea5e11db1c0925efe5ef5fc01d528c522"
uuid = "d9ec5142-1e00-5aa0-9d6a-321866360f50"
version = "0.13.7"

[[NaturalSort]]
git-tree-sha1 = "eda490d06b9f7c00752ee81cfa451efe55521e21"
uuid = "c020b1a1-e9b0-503a-9c33-f039bfc54a85"
version = "1.0.0"

[[NearestNeighbors]]
deps = ["Distances", "StaticArrays"]
git-tree-sha1 = "16baacfdc8758bc374882566c9187e785e85c2f0"
uuid = "b8a86587-4115-5ab1-83bc-aa920d37bbce"
version = "0.4.9"

[[NetworkOptions]]
uuid = "ca575930-c2e3-43a9-ace4-1e988b2c1908"

[[Observables]]
git-tree-sha1 = "fe29afdef3d0c4a8286128d4e45cc50621b1e43d"
uuid = "510215fc-4207-5dde-b226-833fc4488ee2"
version = "0.4.0"

[[OffsetArrays]]
deps = ["Adapt"]
git-tree-sha1 = "043017e0bdeff61cfbb7afeb558ab29536bbb5ed"
uuid = "6fe1bfb0-de20-5000-8ca7-80f57d26f881"
version = "1.10.8"

[[Ogg_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "887579a3eb005446d514ab7aeac5d1d027658b8f"
uuid = "e7412a2a-1a6e-54c0-be00-318e2571c051"
version = "1.3.5+1"

[[OpenBLAS_jll]]
deps = ["Artifacts", "CompilerSupportLibraries_jll", "Libdl"]
uuid = "4536629a-c528-5b80-bd46-f80d51c5b363"

[[OpenLibm_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "05823500-19ac-5b8b-9628-191a04bc5112"

[[OpenSSL_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "648107615c15d4e09f7eca16307bc821c1f718d8"
uuid = "458c3c95-2e84-50aa-8efc-19380b2a3a95"
version = "1.1.13+0"

[[OpenSpecFun_jll]]
deps = ["Artifacts", "CompilerSupportLibraries_jll", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "13652491f6856acfd2db29360e1bbcd4565d04f1"
uuid = "efe28fd5-8261-553b-a9e1-b2916fc3738e"
version = "0.5.5+0"

[[Optim]]
deps = ["Compat", "FillArrays", "ForwardDiff", "LineSearches", "LinearAlgebra", "NLSolversBase", "NaNMath", "Parameters", "PositiveFactorizations", "Printf", "SparseArrays", "StatsBase"]
git-tree-sha1 = "045d10789f5daff18deb454d5923c6996017c2f3"
uuid = "429524aa-4258-5aef-a3af-852621145aeb"
version = "1.6.1"

[[Opus_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "51a08fb14ec28da2ec7a927c4337e4332c2a4720"
uuid = "91d4177d-7536-5919-b921-800302f37372"
version = "1.3.2+0"

[[OrderedCollections]]
git-tree-sha1 = "85f8e6578bf1f9ee0d11e7bb1b1456435479d47c"
uuid = "bac558e1-5e72-5ebc-8fee-abe8a469f55d"
version = "1.4.1"

[[PCRE_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "b2a7af664e098055a7529ad1a900ded962bca488"
uuid = "2f80f16e-611a-54ab-bc61-aa92de5b98fc"
version = "8.44.0+0"

[[PDMats]]
deps = ["LinearAlgebra", "SparseArrays", "SuiteSparse"]
git-tree-sha1 = "ee26b350276c51697c9c2d88a072b339f9f03d73"
uuid = "90014a1f-27ba-587c-ab20-58faa44d9150"
version = "0.11.5"

[[Parameters]]
deps = ["OrderedCollections", "UnPack"]
git-tree-sha1 = "34c0e9ad262e5f7fc75b10a9952ca7692cfc5fbe"
uuid = "d96e819e-fc66-5662-9728-84c9c7592b0a"
version = "0.12.3"

[[ParetoSmooth]]
deps = ["AxisKeys", "InteractiveUtils", "LinearAlgebra", "LogExpFunctions", "MCMCDiagnosticTools", "NamedDims", "PrettyTables", "Printf", "Random", "Requires", "Statistics", "StatsBase", "Tullio"]
git-tree-sha1 = "c6e1c653d65d9b411f93d173678e82cf086d92e6"
uuid = "a68b5a21-f429-434e-8bfa-46b447300aac"
version = "0.7.0"

[[ParetoSmoothedImportanceSampling]]
deps = ["CSV", "DataFrames", "Distributions", "JSON", "Printf", "Random", "StanSample", "Statistics", "StatsFuns", "StatsPlots", "Test"]
git-tree-sha1 = "d9cc58409aa4dd7cbfdf10bb535bd6c72ad22ce2"
uuid = "98f080ec-61e2-11eb-1c7b-31ea1097256f"
version = "1.3.0"

[[Parsers]]
deps = ["Dates"]
git-tree-sha1 = "0b5cfbb704034b5b4c1869e36634438a047df065"
uuid = "69de0a69-1ddd-5017-9359-2bf0b02dc9f0"
version = "2.2.1"

[[Pixman_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "b4f5d02549a10e20780a24fce72bea96b6329e29"
uuid = "30392449-352a-5448-841d-b1acce4e97dc"
version = "0.40.1+0"

[[Pkg]]
deps = ["Artifacts", "Dates", "Downloads", "LibGit2", "Libdl", "Logging", "Markdown", "Printf", "REPL", "Random", "SHA", "Serialization", "TOML", "Tar", "UUIDs", "p7zip_jll"]
uuid = "44cfe95a-1eb2-52ea-b672-e2afdf69b78f"

[[PlotThemes]]
deps = ["PlotUtils", "Requires", "Statistics"]
git-tree-sha1 = "a3a964ce9dc7898193536002a6dd892b1b5a6f1d"
uuid = "ccf2f8ad-2431-5c83-bf29-c5338b663b6a"
version = "2.0.1"

[[PlotUtils]]
deps = ["ColorSchemes", "Colors", "Dates", "Printf", "Random", "Reexport", "Statistics"]
git-tree-sha1 = "6f1b25e8ea06279b5689263cc538f51331d7ca17"
uuid = "995b91a9-d308-5afd-9ec6-746e21dbc043"
version = "1.1.3"

[[Plots]]
deps = ["Base64", "Contour", "Dates", "Downloads", "FFMPEG", "FixedPointNumbers", "GR", "GeometryBasics", "JSON", "Latexify", "LinearAlgebra", "Measures", "NaNMath", "PlotThemes", "PlotUtils", "Printf", "REPL", "Random", "RecipesBase", "RecipesPipeline", "Reexport", "Requires", "Scratch", "Showoff", "SparseArrays", "Statistics", "StatsBase", "UUIDs", "UnicodeFun", "Unzip"]
git-tree-sha1 = "7e4920a7d4323b8ffc3db184580598450bde8a8e"
uuid = "91a5bcdd-55d7-5caf-9e0b-520d859cae80"
version = "1.25.7"

[[PooledArrays]]
deps = ["DataAPI", "Future"]
git-tree-sha1 = "db3a23166af8aebf4db5ef87ac5b00d36eb771e2"
uuid = "2dfb63ee-cc39-5dd5-95bd-886bf059d720"
version = "1.4.0"

[[PositiveFactorizations]]
deps = ["LinearAlgebra"]
git-tree-sha1 = "17275485f373e6673f7e7f97051f703ed5b15b20"
uuid = "85a6dd25-e78a-55b7-8502-1745935b8125"
version = "0.2.4"

[[Preferences]]
deps = ["TOML"]
git-tree-sha1 = "2cf929d64681236a2e074ffafb8d568733d2e6af"
uuid = "21216c6a-2e73-6563-6e65-726566657250"
version = "1.2.3"

[[PrettyTables]]
deps = ["Crayons", "Formatting", "Markdown", "Reexport", "Tables"]
git-tree-sha1 = "dfb54c4e414caa595a1f2ed759b160f5a3ddcba5"
uuid = "08abe8d2-0d0c-5749-adfa-8a2ac140af0d"
version = "1.3.1"

[[Printf]]
deps = ["Unicode"]
uuid = "de0858da-6303-5e67-8744-51eddeeeb8d7"

[[ProgressLogging]]
deps = ["Logging", "SHA", "UUIDs"]
git-tree-sha1 = "80d919dee55b9c50e8d9e2da5eeafff3fe58b539"
uuid = "33c8b6b6-d38a-422a-b730-caa89a2f386c"
version = "0.1.4"

[[ProgressMeter]]
deps = ["Distributed", "Printf"]
git-tree-sha1 = "afadeba63d90ff223a6a48d2009434ecee2ec9e8"
uuid = "92933f4c-e287-5a05-a399-4b506db050ca"
version = "1.7.1"

[[Qt5Base_jll]]
deps = ["Artifacts", "CompilerSupportLibraries_jll", "Fontconfig_jll", "Glib_jll", "JLLWrappers", "Libdl", "Libglvnd_jll", "OpenSSL_jll", "Pkg", "Xorg_libXext_jll", "Xorg_libxcb_jll", "Xorg_xcb_util_image_jll", "Xorg_xcb_util_keysyms_jll", "Xorg_xcb_util_renderutil_jll", "Xorg_xcb_util_wm_jll", "Zlib_jll", "xkbcommon_jll"]
git-tree-sha1 = "ad368663a5e20dbb8d6dc2fddeefe4dae0781ae8"
uuid = "ea2cea3b-5b76-57ae-a6ef-0a8af62496e1"
version = "5.15.3+0"

[[QuadGK]]
deps = ["DataStructures", "LinearAlgebra"]
git-tree-sha1 = "78aadffb3efd2155af139781b8a8df1ef279ea39"
uuid = "1fd47b50-473d-5c70-9696-f719f8f3bcdc"
version = "2.4.2"

[[REPL]]
deps = ["InteractiveUtils", "Markdown", "Sockets", "Unicode"]
uuid = "3fa0cd96-eef1-5676-8a61-b3b8758bbffb"

[[Random]]
deps = ["Serialization"]
uuid = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"

[[RangeArrays]]
git-tree-sha1 = "b9039e93773ddcfc828f12aadf7115b4b4d225f5"
uuid = "b3c3ace0-ae52-54e7-9d0b-2c1406fd6b9d"
version = "0.3.2"

[[Ratios]]
deps = ["Requires"]
git-tree-sha1 = "01d341f502250e81f6fec0afe662aa861392a3aa"
uuid = "c84ed2f1-dad5-54f0-aa8e-dbefe2724439"
version = "0.4.2"

[[RealDot]]
deps = ["LinearAlgebra"]
git-tree-sha1 = "9f0a1b71baaf7650f4fa8a1d168c7fb6ee41f0c9"
uuid = "c1ae055f-0cd5-4b69-90a6-9a35b1a98df9"
version = "0.1.0"

[[RecipesBase]]
git-tree-sha1 = "6bf3f380ff52ce0832ddd3a2a7b9538ed1bcca7d"
uuid = "3cdcf5f2-1ef4-517c-9805-6587b60abb01"
version = "1.2.1"

[[RecipesPipeline]]
deps = ["Dates", "NaNMath", "PlotUtils", "RecipesBase"]
git-tree-sha1 = "37c1631cb3cc36a535105e6d5557864c82cd8c2b"
uuid = "01d81517-befc-4cb6-b9ec-a95719d0359c"
version = "0.5.0"

[[RecursiveArrayTools]]
deps = ["Adapt", "ArrayInterface", "ChainRulesCore", "DocStringExtensions", "FillArrays", "LinearAlgebra", "RecipesBase", "Requires", "StaticArrays", "Statistics", "ZygoteRules"]
git-tree-sha1 = "5144e1eafb2ecc75765888a4bdcd3a30a6a08b14"
uuid = "731186ca-8d62-57ce-b412-fbd966d074cd"
version = "2.24.1"

[[Reexport]]
git-tree-sha1 = "45e428421666073eab6f2da5c9d310d99bb12f9b"
uuid = "189a3867-3050-52da-a836-e630ba90ab69"
version = "1.2.2"

[[RelocatableFolders]]
deps = ["SHA", "Scratch"]
git-tree-sha1 = "cdbd3b1338c72ce29d9584fdbe9e9b70eeb5adca"
uuid = "05181044-ff0b-4ac5-8273-598c1e38db00"
version = "0.1.3"

[[Requires]]
deps = ["UUIDs"]
git-tree-sha1 = "838a3a4188e2ded87a4f9f184b4b0d78a1e91cb7"
uuid = "ae029012-a4dd-5104-9daa-d747884805df"
version = "1.3.0"

[[Rmath]]
deps = ["Random", "Rmath_jll"]
git-tree-sha1 = "bf3188feca147ce108c76ad82c2792c57abe7b1f"
uuid = "79098fc4-a85e-5d69-aa6a-4863f24498fa"
version = "0.7.0"

[[Rmath_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "68db32dff12bb6127bac73c209881191bf0efbb7"
uuid = "f50d1b31-88e8-58de-be2c-1cc44531875f"
version = "0.3.0+0"

[[Roots]]
deps = ["CommonSolve", "Printf", "Setfield"]
git-tree-sha1 = "0abe7fc220977da88ad86d339335a4517944fea2"
uuid = "f2b01f46-fcfa-551c-844a-d8ac1e96c665"
version = "1.3.14"

[[SHA]]
uuid = "ea8e919c-243c-51af-8825-aaa63cd721ce"

[[SIMDTypes]]
git-tree-sha1 = "330289636fb8107c5f32088d2741e9fd7a061a5c"
uuid = "94e857df-77ce-4151-89e5-788b33177be4"
version = "0.1.0"

[[SLEEFPirates]]
deps = ["IfElse", "Static", "VectorizationBase"]
git-tree-sha1 = "1410aad1c6b35862573c01b96cd1f6dbe3979994"
uuid = "476501e8-09a2-5ece-8869-fb82de89a1fa"
version = "0.6.28"

[[SciMLBase]]
deps = ["ArrayInterface", "CommonSolve", "ConstructionBase", "Distributed", "DocStringExtensions", "IteratorInterfaceExtensions", "LinearAlgebra", "Logging", "RecipesBase", "RecursiveArrayTools", "StaticArrays", "Statistics", "Tables", "TreeViews"]
git-tree-sha1 = "f4862c0cb4e34ed182718221028ba1bf50742108"
uuid = "0bca4576-84f4-4d90-8ffe-ffa030f20462"
version = "1.26.1"

[[ScientificTypesBase]]
git-tree-sha1 = "a8e18eb383b5ecf1b5e6fc237eb39255044fd92b"
uuid = "30f210dd-8aff-4c5f-94ba-8e64358c1161"
version = "3.0.0"

[[Scratch]]
deps = ["Dates"]
git-tree-sha1 = "0b4b7f1393cff97c33891da2a0bf69c6ed241fda"
uuid = "6c6a2e73-6563-6170-7368-637461726353"
version = "1.1.0"

[[SentinelArrays]]
deps = ["Dates", "Random"]
git-tree-sha1 = "15dfe6b103c2a993be24404124b8791a09460983"
uuid = "91c51154-3ec4-41a3-a24f-3f23e20d615c"
version = "1.3.11"

[[Serialization]]
uuid = "9e88b42a-f829-5b0c-bbe9-9e923198166b"

[[Setfield]]
deps = ["ConstructionBase", "Future", "MacroTools", "Requires"]
git-tree-sha1 = "0afd9e6c623e379f593da01f20590bacc26d1d14"
uuid = "efcf1570-3423-57d1-acb7-fd33fddbac46"
version = "0.8.1"

[[SharedArrays]]
deps = ["Distributed", "Mmap", "Random", "Serialization"]
uuid = "1a1011a3-84de-559e-8e89-a11a2f7dc383"

[[Showoff]]
deps = ["Dates", "Grisu"]
git-tree-sha1 = "91eddf657aca81df9ae6ceb20b959ae5653ad1de"
uuid = "992d4aef-0814-514b-bc4d-f2e9a6c4116f"
version = "1.0.3"

[[Sockets]]
uuid = "6462fe0b-24de-5631-8697-dd941f90decc"

[[SortingAlgorithms]]
deps = ["DataStructures"]
git-tree-sha1 = "b3363d7460f7d098ca0912c69b082f75625d7508"
uuid = "a2af1166-a08f-5f64-846c-94a0d3cef48c"
version = "1.0.1"

[[SparseArrays]]
deps = ["LinearAlgebra", "Random"]
uuid = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"

[[SpecialFunctions]]
deps = ["ChainRulesCore", "IrrationalConstants", "LogExpFunctions", "OpenLibm_jll", "OpenSpecFun_jll"]
git-tree-sha1 = "a4116accb1c84f0a8e1b9932d873654942b2364b"
uuid = "276daf66-3868-5448-9aa4-cd146d93841b"
version = "2.1.1"

[[SplittablesBase]]
deps = ["Setfield", "Test"]
git-tree-sha1 = "39c9f91521de844bad65049efd4f9223e7ed43f9"
uuid = "171d559e-b47b-412a-8079-5efa626c420e"
version = "0.1.14"

[[StanBase]]
deps = ["CSV", "DataFrames", "DelimitedFiles", "Distributed", "DocStringExtensions", "Documenter", "Parameters", "Random", "StanDump", "Unicode"]
git-tree-sha1 = "0ad37706160da3c5a08b6429f2b4bc078abc479d"
uuid = "d0ee94f6-a23d-54aa-bbe9-7f572d6da7f5"
version = "3.4.0"

[[StanDump]]
deps = ["ArgCheck", "DocStringExtensions"]
git-tree-sha1 = "bfaebe19ada44a52a6c797d48473f1bb22fd0853"
uuid = "9713c8f3-0168-54b5-986e-22c526958f39"
version = "0.2.0"

[[StanSample]]
deps = ["CSV", "DataFrames", "DelimitedFiles", "Distributed", "DocStringExtensions", "MonteCarloMeasurements", "NamedTupleTools", "OrderedCollections", "Parameters", "Random", "Reexport", "Requires", "StanBase", "StanDump", "TableOperations", "Tables", "Unicode"]
git-tree-sha1 = "4f1521585e5a93cdb1d5abf80427527837f952d9"
uuid = "c1514b29-d3a0-5178-b312-660c88baa699"
version = "5.6.0"

[[Static]]
deps = ["IfElse"]
git-tree-sha1 = "a8f30abc7c64a39d389680b74e749cf33f872a70"
uuid = "aedffcd0-7271-4cad-89d0-dc628f76c6d3"
version = "0.3.3"

[[StaticArrays]]
deps = ["LinearAlgebra", "Random", "Statistics"]
git-tree-sha1 = "a635a9333989a094bddc9f940c04c549cd66afcf"
uuid = "90137ffa-7385-5640-81b9-e52037218182"
version = "1.3.4"

[[StatisticalRethinking]]
deps = ["AxisKeys", "CSV", "DataFrames", "Dates", "Distributions", "DocStringExtensions", "Documenter", "Formatting", "KernelDensity", "LinearAlgebra", "MCMCChains", "MonteCarloMeasurements", "NamedArrays", "NamedTupleTools", "Optim", "OrderedCollections", "Parameters", "ParetoSmooth", "ParetoSmoothedImportanceSampling", "PrettyTables", "Random", "Reexport", "Requires", "Statistics", "StatsBase", "StatsFuns", "StructuralCausalModels", "Tables", "Test", "Unicode"]
git-tree-sha1 = "b0bb5b9b958ae5174915271fed6a8f52cca5e549"
uuid = "2d09df54-9d0f-5258-8220-54c2a3d4fbee"
version = "4.5.0"

[[StatisticalTraits]]
deps = ["ScientificTypesBase"]
git-tree-sha1 = "271a7fea12d319f23d55b785c51f6876aadb9ac0"
uuid = "64bff920-2084-43da-a3e6-9bb72801c0c9"
version = "3.0.0"

[[Statistics]]
deps = ["LinearAlgebra", "SparseArrays"]
uuid = "10745b16-79ce-11e8-11f9-7d13ad32a3b2"

[[StatsAPI]]
git-tree-sha1 = "d88665adc9bcf45903013af0982e2fd05ae3d0a6"
uuid = "82ae8749-77ed-4fe6-ae5f-f523153014b0"
version = "1.2.0"

[[StatsBase]]
deps = ["DataAPI", "DataStructures", "LinearAlgebra", "LogExpFunctions", "Missings", "Printf", "Random", "SortingAlgorithms", "SparseArrays", "Statistics", "StatsAPI"]
git-tree-sha1 = "51383f2d367eb3b444c961d485c565e4c0cf4ba0"
uuid = "2913bbd2-ae8a-5f71-8c99-4fb6c76f3a91"
version = "0.33.14"

[[StatsFuns]]
deps = ["ChainRulesCore", "InverseFunctions", "IrrationalConstants", "LogExpFunctions", "Reexport", "Rmath", "SpecialFunctions"]
git-tree-sha1 = "f35e1879a71cca95f4826a14cdbf0b9e253ed918"
uuid = "4c63d2b9-4356-54db-8cca-17b64c39e42c"
version = "0.9.15"

[[StatsPlots]]
deps = ["AbstractFFTs", "Clustering", "DataStructures", "DataValues", "Distributions", "Interpolations", "KernelDensity", "LinearAlgebra", "MultivariateStats", "Observables", "Plots", "RecipesBase", "RecipesPipeline", "Reexport", "StatsBase", "TableOperations", "Tables", "Widgets"]
git-tree-sha1 = "e0eef8106b34449a42ae521eb174683f710804a7"
uuid = "f3b207a7-027a-5e70-b257-86293d7955fd"
version = "0.14.31"

[[StructArrays]]
deps = ["Adapt", "DataAPI", "StaticArrays", "Tables"]
git-tree-sha1 = "d21f2c564b21a202f4677c0fba5b5ee431058544"
uuid = "09ab397b-f2b6-538f-b94a-2f83cf4a842a"
version = "0.6.4"

[[StructuralCausalModels]]
deps = ["CSV", "Combinatorics", "DataFrames", "DataStructures", "Distributions", "DocStringExtensions", "LinearAlgebra", "NamedArrays", "Reexport", "Statistics"]
git-tree-sha1 = "3fde9925915106192dbd99484cebaa7489c38f23"
uuid = "a41e6734-49ce-4065-8b83-aff084c01dfd"
version = "1.3.0"

[[SuiteSparse]]
deps = ["Libdl", "LinearAlgebra", "Serialization", "SparseArrays"]
uuid = "4607b0f0-06f3-5cda-b6b1-a6196a1729e9"

[[TOML]]
deps = ["Dates"]
uuid = "fa267f1f-6049-4f14-aa54-33bafae1ed76"

[[TableOperations]]
deps = ["SentinelArrays", "Tables", "Test"]
git-tree-sha1 = "e383c87cf2a1dc41fa30c093b2a19877c83e1bc1"
uuid = "ab02a1b2-a7df-11e8-156e-fb1833f50b87"
version = "1.2.0"

[[TableTraits]]
deps = ["IteratorInterfaceExtensions"]
git-tree-sha1 = "c06b2f539df1c6efa794486abfb6ed2022561a39"
uuid = "3783bdb8-4a98-5b6b-af9a-565f29a5fe9c"
version = "1.0.1"

[[Tables]]
deps = ["DataAPI", "DataValueInterfaces", "IteratorInterfaceExtensions", "LinearAlgebra", "TableTraits", "Test"]
git-tree-sha1 = "bb1064c9a84c52e277f1096cf41434b675cd368b"
uuid = "bd369af6-aec1-5ad0-b16a-f7cc5008161c"
version = "1.6.1"

[[Tar]]
deps = ["ArgTools", "SHA"]
uuid = "a4e569a6-e804-4fa4-b0f3-eef7a1d5b13e"

[[TerminalLoggers]]
deps = ["LeftChildRightSiblingTrees", "Logging", "Markdown", "Printf", "ProgressLogging", "UUIDs"]
git-tree-sha1 = "62846a48a6cd70e63aa29944b8c4ef704360d72f"
uuid = "5d786b92-1e48-4d6f-9151-6b4477ca9bed"
version = "0.1.5"

[[Test]]
deps = ["InteractiveUtils", "Logging", "Random", "Serialization"]
uuid = "8dfed614-e22c-5e08-85e1-65c5234f0b40"

[[Tracker]]
deps = ["Adapt", "DiffRules", "ForwardDiff", "LinearAlgebra", "LogExpFunctions", "MacroTools", "NNlib", "NaNMath", "Printf", "Random", "Requires", "SpecialFunctions", "Statistics"]
git-tree-sha1 = "7b00adbe4216b919d487d82a852c48f378c6ed37"
uuid = "9f7883ad-71c0-57eb-9f7f-b5c9e6d3789c"
version = "0.2.18"

[[TranscodingStreams]]
deps = ["Random", "Test"]
git-tree-sha1 = "216b95ea110b5972db65aa90f88d8d89dcb8851c"
uuid = "3bb67fe8-82b1-5028-8e26-92a6c54297fa"
version = "0.9.6"

[[Transducers]]
deps = ["Adapt", "ArgCheck", "BangBang", "Baselet", "CompositionsBase", "DefineSingletons", "Distributed", "InitialValues", "Logging", "Markdown", "MicroCollections", "Requires", "Setfield", "SplittablesBase", "Tables"]
git-tree-sha1 = "1cda71cc967e3ef78aa2593319f6c7379376f752"
uuid = "28d57a85-8fef-5791-bfe6-a80928e7c999"
version = "0.4.72"

[[TreeViews]]
deps = ["Test"]
git-tree-sha1 = "8d0d7a3fe2f30d6a7f833a5f19f7c7a5b396eae6"
uuid = "a2a6695c-b41b-5b7d-aed9-dbfdeacea5d7"
version = "0.3.0"

[[Tullio]]
deps = ["ChainRulesCore", "DiffRules", "LinearAlgebra", "Requires"]
git-tree-sha1 = "7830c974acc69437a3fee35dd7b510a74cbc862d"
uuid = "bc48ee85-29a4-5162-ae0b-a64e1601d4bc"
version = "0.3.3"

[[Turing]]
deps = ["AbstractMCMC", "AdvancedHMC", "AdvancedMH", "AdvancedPS", "AdvancedVI", "BangBang", "Bijectors", "DataStructures", "Distributions", "DistributionsAD", "DocStringExtensions", "DynamicPPL", "EllipticalSliceSampling", "ForwardDiff", "Libtask", "LinearAlgebra", "MCMCChains", "NamedArrays", "Printf", "Random", "Reexport", "Requires", "SciMLBase", "SpecialFunctions", "Statistics", "StatsBase", "StatsFuns", "Tracker", "ZygoteRules"]
git-tree-sha1 = "602c61b74cc96832eaf12eb0a19b911d5f1bd6a4"
uuid = "fce5fe82-541a-59a6-adf8-730c64b5f9a0"
version = "0.20.0"

[[URIs]]
git-tree-sha1 = "97bbe755a53fe859669cd907f2d96aee8d2c1355"
uuid = "5c2747f8-b7ea-4ff2-ba2e-563bfd36b1d4"
version = "1.3.0"

[[UUIDs]]
deps = ["Random", "SHA"]
uuid = "cf7118a7-6976-5b1a-9a39-7adc72f591a4"

[[UnPack]]
git-tree-sha1 = "387c1f73762231e86e0c9c5443ce3b4a0a9a0c2b"
uuid = "3a884ed6-31ef-47d7-9d2a-63182c4928ed"
version = "1.0.2"

[[Unicode]]
uuid = "4ec0a83e-493e-50e2-b9ac-8f72acf5a8f5"

[[UnicodeFun]]
deps = ["REPL"]
git-tree-sha1 = "53915e50200959667e78a92a418594b428dffddf"
uuid = "1cfade01-22cf-5700-b092-accc4b62d6e1"
version = "0.4.1"

[[Unzip]]
git-tree-sha1 = "34db80951901073501137bdbc3d5a8e7bbd06670"
uuid = "41fe7b60-77ed-43a1-b4f0-825fd5a5650d"
version = "0.1.2"

[[VectorizationBase]]
deps = ["ArrayInterface", "CPUSummary", "HostCPUFeatures", "Hwloc", "IfElse", "LayoutPointers", "Libdl", "LinearAlgebra", "SIMDTypes", "Static"]
git-tree-sha1 = "e9a35d501b24c127af57ca5228bcfb806eda7507"
uuid = "3d5dd08c-fd9d-11e8-17fa-ed2836048c2f"
version = "0.21.24"

[[Wayland_jll]]
deps = ["Artifacts", "Expat_jll", "JLLWrappers", "Libdl", "Libffi_jll", "Pkg", "XML2_jll"]
git-tree-sha1 = "3e61f0b86f90dacb0bc0e73a0c5a83f6a8636e23"
uuid = "a2964d1f-97da-50d4-b82a-358c7fce9d89"
version = "1.19.0+0"

[[Wayland_protocols_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "66d72dc6fcc86352f01676e8f0f698562e60510f"
uuid = "2381bf8a-dfd0-557d-9999-79630e7b1b91"
version = "1.23.0+0"

[[WeakRefStrings]]
deps = ["DataAPI", "InlineStrings", "Parsers"]
git-tree-sha1 = "c69f9da3ff2f4f02e811c3323c22e5dfcb584cfa"
uuid = "ea10d353-3f73-51f8-a26c-33c1cb351aa5"
version = "1.4.1"

[[Widgets]]
deps = ["Colors", "Dates", "Observables", "OrderedCollections"]
git-tree-sha1 = "80661f59d28714632132c73779f8becc19a113f2"
uuid = "cc8bc4a8-27d6-5769-a93b-9d913e69aa62"
version = "0.6.4"

[[WoodburyMatrices]]
deps = ["LinearAlgebra", "SparseArrays"]
git-tree-sha1 = "de67fa59e33ad156a590055375a30b23c40299d3"
uuid = "efce3f68-66dc-5838-9240-27a6d6f5f9b6"
version = "0.5.5"

[[XML2_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Libiconv_jll", "Pkg", "Zlib_jll"]
git-tree-sha1 = "1acf5bdf07aa0907e0a37d3718bb88d4b687b74a"
uuid = "02c8fc9c-b97f-50b9-bbe4-9be30ff0a78a"
version = "2.9.12+0"

[[XSLT_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Libgcrypt_jll", "Libgpg_error_jll", "Libiconv_jll", "Pkg", "XML2_jll", "Zlib_jll"]
git-tree-sha1 = "91844873c4085240b95e795f692c4cec4d805f8a"
uuid = "aed1982a-8fda-507f-9586-7b0439959a61"
version = "1.1.34+0"

[[Xorg_libX11_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libxcb_jll", "Xorg_xtrans_jll"]
git-tree-sha1 = "5be649d550f3f4b95308bf0183b82e2582876527"
uuid = "4f6342f7-b3d2-589e-9d20-edeb45f2b2bc"
version = "1.6.9+4"

[[Xorg_libXau_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "4e490d5c960c314f33885790ed410ff3a94ce67e"
uuid = "0c0b7dd1-d40b-584c-a123-a41640f87eec"
version = "1.0.9+4"

[[Xorg_libXcursor_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXfixes_jll", "Xorg_libXrender_jll"]
git-tree-sha1 = "12e0eb3bc634fa2080c1c37fccf56f7c22989afd"
uuid = "935fb764-8cf2-53bf-bb30-45bb1f8bf724"
version = "1.2.0+4"

[[Xorg_libXdmcp_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "4fe47bd2247248125c428978740e18a681372dd4"
uuid = "a3789734-cfe1-5b06-b2d0-1dd0d9d62d05"
version = "1.1.3+4"

[[Xorg_libXext_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll"]
git-tree-sha1 = "b7c0aa8c376b31e4852b360222848637f481f8c3"
uuid = "1082639a-0dae-5f34-9b06-72781eeb8cb3"
version = "1.3.4+4"

[[Xorg_libXfixes_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll"]
git-tree-sha1 = "0e0dc7431e7a0587559f9294aeec269471c991a4"
uuid = "d091e8ba-531a-589c-9de9-94069b037ed8"
version = "5.0.3+4"

[[Xorg_libXi_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXext_jll", "Xorg_libXfixes_jll"]
git-tree-sha1 = "89b52bc2160aadc84d707093930ef0bffa641246"
uuid = "a51aa0fd-4e3c-5386-b890-e753decda492"
version = "1.7.10+4"

[[Xorg_libXinerama_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXext_jll"]
git-tree-sha1 = "26be8b1c342929259317d8b9f7b53bf2bb73b123"
uuid = "d1454406-59df-5ea1-beac-c340f2130bc3"
version = "1.1.4+4"

[[Xorg_libXrandr_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXext_jll", "Xorg_libXrender_jll"]
git-tree-sha1 = "34cea83cb726fb58f325887bf0612c6b3fb17631"
uuid = "ec84b674-ba8e-5d96-8ba1-2a689ba10484"
version = "1.5.2+4"

[[Xorg_libXrender_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll"]
git-tree-sha1 = "19560f30fd49f4d4efbe7002a1037f8c43d43b96"
uuid = "ea2f1a96-1ddc-540d-b46f-429655e07cfa"
version = "0.9.10+4"

[[Xorg_libpthread_stubs_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "6783737e45d3c59a4a4c4091f5f88cdcf0908cbb"
uuid = "14d82f49-176c-5ed1-bb49-ad3f5cbd8c74"
version = "0.1.0+3"

[[Xorg_libxcb_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "XSLT_jll", "Xorg_libXau_jll", "Xorg_libXdmcp_jll", "Xorg_libpthread_stubs_jll"]
git-tree-sha1 = "daf17f441228e7a3833846cd048892861cff16d6"
uuid = "c7cfdc94-dc32-55de-ac96-5a1b8d977c5b"
version = "1.13.0+3"

[[Xorg_libxkbfile_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll"]
git-tree-sha1 = "926af861744212db0eb001d9e40b5d16292080b2"
uuid = "cc61e674-0454-545c-8b26-ed2c68acab7a"
version = "1.1.0+4"

[[Xorg_xcb_util_image_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"]
git-tree-sha1 = "0fab0a40349ba1cba2c1da699243396ff8e94b97"
uuid = "12413925-8142-5f55-bb0e-6d7ca50bb09b"
version = "0.4.0+1"

[[Xorg_xcb_util_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libxcb_jll"]
git-tree-sha1 = "e7fd7b2881fa2eaa72717420894d3938177862d1"
uuid = "2def613f-5ad1-5310-b15b-b15d46f528f5"
version = "0.4.0+1"

[[Xorg_xcb_util_keysyms_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"]
git-tree-sha1 = "d1151e2c45a544f32441a567d1690e701ec89b00"
uuid = "975044d2-76e6-5fbe-bf08-97ce7c6574c7"
version = "0.4.0+1"

[[Xorg_xcb_util_renderutil_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"]
git-tree-sha1 = "dfd7a8f38d4613b6a575253b3174dd991ca6183e"
uuid = "0d47668e-0667-5a69-a72c-f761630bfb7e"
version = "0.3.9+1"

[[Xorg_xcb_util_wm_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"]
git-tree-sha1 = "e78d10aab01a4a154142c5006ed44fd9e8e31b67"
uuid = "c22f9ab0-d5fe-5066-847c-f4bb1cd4e361"
version = "0.4.1+1"

[[Xorg_xkbcomp_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libxkbfile_jll"]
git-tree-sha1 = "4bcbf660f6c2e714f87e960a171b119d06ee163b"
uuid = "35661453-b289-5fab-8a00-3d9160c6a3a4"
version = "1.4.2+4"

[[Xorg_xkeyboard_config_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xkbcomp_jll"]
git-tree-sha1 = "5c8424f8a67c3f2209646d4425f3d415fee5931d"
uuid = "33bec58e-1273-512f-9401-5d533626f822"
version = "2.27.0+4"

[[Xorg_xtrans_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "79c31e7844f6ecf779705fbc12146eb190b7d845"
uuid = "c5fb5394-a638-5e4d-96e5-b29de1b5cf10"
version = "1.4.0+3"

[[Zlib_jll]]
deps = ["Libdl"]
uuid = "83775a58-1f1d-513f-b197-d71354ab007a"

[[Zstd_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "cc4bf3fdde8b7e3e9fa0351bdeedba1cf3b7f6e6"
uuid = "3161d3a3-bdf6-5164-811a-617609db77b4"
version = "1.5.0+0"

[[ZygoteRules]]
deps = ["MacroTools"]
git-tree-sha1 = "8c1a8e4dfacb1fd631745552c8db35d0deb09ea0"
uuid = "700de1a5-db45-46bc-99cf-38207098b444"
version = "0.2.2"

[[libass_jll]]
deps = ["Artifacts", "Bzip2_jll", "FreeType2_jll", "FriBidi_jll", "HarfBuzz_jll", "JLLWrappers", "Libdl", "Pkg", "Zlib_jll"]
git-tree-sha1 = "5982a94fcba20f02f42ace44b9894ee2b140fe47"
uuid = "0ac62f75-1d6f-5e53-bd7c-93b484bb37c0"
version = "0.15.1+0"

[[libfdk_aac_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "daacc84a041563f965be61859a36e17c4e4fcd55"
uuid = "f638f0a6-7fb0-5443-88ba-1cc74229b280"
version = "2.0.2+0"

[[libpng_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Zlib_jll"]
git-tree-sha1 = "94d180a6d2b5e55e447e2d27a29ed04fe79eb30c"
uuid = "b53b4c65-9356-5827-b1ea-8c7a1a84506f"
version = "1.6.38+0"

[[libvorbis_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Ogg_jll", "Pkg"]
git-tree-sha1 = "b910cb81ef3fe6e78bf6acee440bda86fd6ae00c"
uuid = "f27f6e37-5d2b-51aa-960f-b287f2bc3b7a"
version = "1.3.7+1"

[[nghttp2_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "8e850ede-7688-5339-a07c-302acd2aaf8d"

[[p7zip_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "3f19e933-33d8-53b3-aaab-bd5110c3b7a0"

[[x264_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "4fea590b89e6ec504593146bf8b988b2c00922b2"
uuid = "1270edf5-f2f9-52d2-97e9-ab00b5d0237a"
version = "2021.5.5+0"

[[x265_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "ee567a171cce03570d77ad3a43e90218e38937a9"
uuid = "dfaa095f-4041-5dcd-9319-2fabd8486b76"
version = "3.5.0+0"

[[xkbcommon_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Wayland_jll", "Wayland_protocols_jll", "Xorg_libxcb_jll", "Xorg_xkeyboard_config_jll"]
git-tree-sha1 = "ece2350174195bb31de1a63bea3a41ae1aa593b6"
uuid = "d8fb68d0-12a3-5cfd-a85a-d49703b185fd"
version = "0.9.1+5"
"""

# ╔═╡ Cell order:
# ╟─e1b18f33-19ba-4fb3-a476-47cfeb6345af
# ╟─eef1e512-8579-11ec-1837-0f04dc618fcb
# ╟─3b7e0e99-5e48-4141-ac36-d855ba7aa0bf
# ╟─edec49f8-576f-470a-bcae-2040a688e987
# ╠═9d556aef-e773-4f8d-b220-4f0de53d5c41
# ╠═d36eab23-6ae5-4e54-be78-8901839bbc49
# ╠═4f7b0614-729f-4745-9f1a-e3eb255ea7cc
# ╠═7c307991-87d0-4a85-a3fc-26ed21ae319d
# ╟─f57e4624-d679-4866-b95d-f0b2bc4436e0
# ╠═d9e79634-8d9f-460a-bd1e-e3471dc82bcd
# ╠═9ad28f14-1545-4141-a192-6d3adc1b4f48
# ╠═19954116-525f-4caa-b66d-748dd581bfaa
# ╠═22e0b5a2-663a-49eb-a4f6-fa36353186fc
# ╠═11c077f4-5294-4d26-98fa-a35e3e8116f1
# ╠═115341f3-7d46-456f-9d7a-3ed41fbdafcd
# ╠═c6e67570-ab0b-4213-8bbf-f9b0361ba802
# ╠═4e8a4bef-c071-4934-91b8-aee0416e342a
# ╠═23d7011f-514a-4eb5-a509-5db22e852b0e
# ╠═a0862af8-39c9-426b-a979-3ea1af8ed579
# ╠═e0084ff1-0443-418d-a36a-fd67d0c61659
# ╠═16285a48-97b4-4bcf-b69a-40d4d8e3d575
# ╟─5cea4149-3003-4716-8db8-fb684f8db7c4
# ╟─00000000-0000-0000-0000-000000000001
# ╟─00000000-0000-0000-0000-000000000002

max_stars_repo_path: Bayesian inference.jl

max_stars_repo_name: delphinH/imagetoy

max_issues_repo_path: Bayesian inference.jl

max_issues_repo_name: delphinH/imagetoy

max_forks_repo_path: Bayesian inference.jl

max_forks_repo_name: delphinH/imagetoy


text:
function save_counts(agg, term)
    levelcounts = zeros(maximum(agg), 2)
    for i in 1:maximum(agg)
        levelcounts[i, :] = [i, sum(level_bools(i, agg, term))]
    end
    levelcounts = convert(Matrix{Int64}, levelcounts)
    writedlm("../../data/source/levelcounts.csv", levelcounts, ',')
end

ext: jl

max_stars_repo_name: jungangl/forecast-machine-learning

max_issues_repo_name: jungangl/forecast-machine-learning

max_forks_repo_name: jungangl/forecast-machine-learning


text:
# Use baremodule to shave off a few KB from the serialized `.ji` file
baremodule ALPS_jll
using Base
using Base: UUID
import JLLWrappers

JLLWrappers.@generate_main_file_header("ALPS")
JLLWrappers.@generate_main_file("ALPS", UUID("6a88e26e-56cb-5037-a572-1ff8e7f440e8"))
end  # module ALPS_jll


text:
module Properties

using MacroTools: @capture, postwalk, striplines

export @property

## Macro to generate properties

macro property(rawexpr)
    ex = (rawexpr)

    signature = nothing
    stype = nothing
    reduce_op = nothing
    preallocator = nothing
    has_sources = has_targets = false

    postwalk(ex) do x
        @capture(x, signature = f_) && (signature = f)
        @capture(x, stype = t_)             && (stype = t)
        @capture(x, reduce = op_)           && (reduce_op = op)
        @capture(x, preallocator = p_)      && (preallocator = p)

        has_sources |= @capture(x, _::Source)
        has_targets |= @capture(x, _::Target)

        return x
    end

    if nothing === signature
        throw(ArgumentError("missing `signature = ...` entry"))
    end

    if !(@capture(signature, _(__)))
        throw(ArgumentError("signature must look like a function call"))
    end

    if has_sources && has_targets
        return esc(induced_property(signature, stype, preallocator))
    elseif has_sources
        return esc(source_property(signature, stype, reduce_op))
    else
        throw(ArgumentError("missing at least one `::Source` argument in signature"))
    end
end

function source_property(signature, stype, reduce_op)
    source_ind = findfirst(x -> isa(x, Expr) && (x.args[2] == :Source), signature.args[2:end])
    source_name = signature.args[source_ind+1].args[1]

    @capture(postwalk(signature) do ex
             @capture(ex, s_::Source) && (return s)
             ex
             end, fname_(fargs__))

    @capture(postwalk(signature) do ex
             @capture(ex, s_::Source) && (return :(Elements.unwrap_targ($s)))
             ex
             end, _(unwrappedargs__))

    if nothing === reduce_op
        mappedvars = Symbol[]
        mappedsyms = Symbol[]

        @capture(postwalk(signature) do ex
                 if @capture(ex, s_::Source)
                     sym = gensym(s)
                     push!(mappedvars, s)
                     push!(mappedsyms, sym)
                     return sym
                 end
                 ex
                 end, _(mappedargs__))

        fgroup = quote
            function $fname($(fargs...), ::Type{Elements.Group})
                map($(mappedvars...)) do $(mappedsyms...)
                    $fname($(mappedargs...))
                end
            end
        end
    else
        op = reduce_op
        if isa(op, Expr) && (op.head == :tuple)
            init_val = op.args[2]
            op = op.args[1]
        else
            init_val = :(zero($stype))
        end

        sumvar = gensym(:Σ)
        index = gensym(:i)

        iterated_call = postwalk(signature) do ex
            @capture(ex, s_::Source) && (return :($s[$index]))
            ex
        end

        fgroup = quote
            function $fname($(fargs...), ::Type{Elements.Group})
                $sumvar = $init_val
                for $index in eachindex($source_name)
                    $sumvar = $op($sumvar, $iterated_call)
                end
                $sumvar
            end
        end
    end

    quote
        Core.@__doc__ function $fname($(fargs...))
            $fname($(unwrappedargs...), Elements.kind(Elements.unwrap_src($source_name)))
        end

        $fgroup
    end
end

function induced_property(signature, stype, preallocator)

    Σ = gensym(:Σ)
    index = gensym(:i)

    @capture(postwalk(signature) do ex
             @capture(ex, t_::Target) && (return t)
             @capture(ex, s_::Source) && (return s)
             ex
             end, fname_(fargs__))
    fname! = Symbol(fname, "!")

    f_allocate = preallocator

    @capture(postwalk(signature) do ex
             @capture(ex, t_::Target) && (return :(Elements.unwrap_targ($t)))
             @capture(ex, s_::Source) && (return :(Elements.unwrap_targ($s)))
             ex
             end, _(unwrappedargs__))

    @capture(postwalk(signature) do ex
             @capture(ex, s_::Source) && (return :($s[$index]))
             @capture(ex, t_::Target) && (return t)
             ex
             end, _(iteratedsources__))

    @capture(postwalk(signature) do ex
             @capture(ex, s_::Source) && (return s)
             @capture(ex, t_::Target) && (return :($t[$index]))
             ex
             end, _(iteratedtargets__))

    @capture(postwalk(signature) do ex
             @capture(ex, t_::Target) && (return :($t::Tuple))
             @capture(ex, s_::Source) && (return s)
             ex
             end, _(targettuples__))

    target_ind = findfirst(x -> isa(x, Expr) && (x.args[2] == :Target), signature.args[2:end])
    target_name = signature.args[target_ind+1].args[1]

    source_ind = findfirst(x -> isa(x, Expr) && (x.args[2] == :Source), signature.args[2:end])
    source_name = signature.args[source_ind+1].args[1]

    position_args = copy(fargs)
    position_args[target_ind] = :(Elements.position($target_name))

    quote
        $f_allocate(group::Tuple) = map($f_allocate, group)

        function $f_allocate($target_name)
            $f_allocate(Elements.unwrap_targ($target_name), Elements.kind(eltype(Elements.unwrap_targ($target_name))))
        end

        $f_allocate($target_name, el::Type{Elements.Singleton}) = zeros($stype, size($target_name))

        Core.@__doc__ function $fname($(fargs...))
            $fname($(unwrappedargs...),
                   Elements.kind(Elements.unwrap_targ($target_name)),
                   Elements.kind(Elements.unwrap_src($source_name)))
        end

        Core.@__doc__ function $fname!(out, $(fargs...))
            $fname!(out, $(unwrappedargs...),
                    Elements.kind(Elements.unwrap_targ($target_name)),
                    Elements.kind(Elements.unwrap_src($source_name)))
        end

        function $fname($(fargs...), ::Type{Elements.Singleton}, ::Type{Elements.Singleton})
            $fname($(position_args...))
        end

        function $fname($(fargs...), ::Type{Elements.Singleton}, ::Type{Elements.Group})
            $Σ = zero($stype)
            for $index in eachindex($source_name)
                $Σ += $fname($(iteratedsources...))
            end
            $Σ
        end

        function $fname($(fargs...), ::Type{Elements.Group}, ::Any)
            out = $f_allocate($target_name)
            $fname!(out, $(fargs...))
        end

        function $fname!(out, $(fargs...), ::Type{Elements.Group}, ::Any)
            for $index in eachindex($target_name)
                out[$index] += $fname($(iteratedtargets...))
            end
            out
        end

        function $fname!(out::Tuple, $(targettuples...))
            for $index in eachindex($target_name)
                $fname!(out[$index], $(iteratedtargets...))
            end
            out
        end
    end
end

end


text:
export ProductionModel, ObservationProduce, ObservationGroupProduce, DataProduce

"Production"
struct ProductionModel <: AbstractProductionModel end

# Abstract data strucutres
#---------------------------

struct ObservationProduce{PM<:ProductionModel,T<:Real, V1<:AbstractVector{T}, V2<:AbstractVector{T}, M <:AbstractMatrix{T}} <: AbstractObservation
    model::PM
    y::V1
    x::M
    xsum::V2
    nu::V1
    xpnu::V2
    nusum::T
    nusumsq::T
    function ObservationProduce(model::PM, y::V1, x::M, xsum::V2, nu::V1, xpnu::V2,nusum::T,nusumsq::T) where {PM<:ProductionModel,T<:Real, V1<:AbstractVector{T}, V2<:AbstractVector{T}, M <:AbstractMatrix{T}}
        k,n = size(x)
        length(nu) == length(y) == n  || throw(DimensionMismatch())
        size(xpnu,1) == size(xsum,1) == k || throw(DimensionMismatch())
        return new{PM,T,V1,V2,M}(model,y,x,xsum,nu,xpnu,nusum,nusumsq)
    end
end

struct DataProduce{M<:ProductionModel,T<:Real} <: AbstractDataSet
    model::M
    y::Vector{T}
    x::Matrix{T}
    xsum::Matrix{T}
    nu::Vector{T}
    xpnu::Matrix{T}

    nusum::Vector{T}
    nusumsq::Vector{T}

    obs_ptr::Vector{Int}
    group_ptr::Vector{Int}
    function DataProduce(
        model::M, y::Vector{T}, x::Matrix{T}, xsum::Matrix{T}, nu::Vector{T}, xpnu::Matrix{T},
        nusum::Vector{T}, nusumsq::Vector{T}, obs_ptr::Vector{Int}, group_ptr::Vector{Int}
    ) where {M<:ProductionModel,T<:Real}
        k,n = size(x)
        length(nu) == length(y) == n  || throw(DimensionMismatch())
        size(xsum,1) == k || throw(DimensionMismatch())
        size(xpnu) == size(xsum) || throw(DimensionMismatch())
        issorted(obs_ptr) || throw(error("obs_ptr not sorted"))
        issorted(group_ptr) || throw(error("group_ptr not sorted"))
        length(nusum)+1 == length(nusumsq)+1 == last(group_ptr) == length(obs_ptr) || throw(DimensionMismatch("last(group_ptr)-1 != length(obs_ptr)"))
        last(obs_ptr)-1 == n || throw(DimensionMismatch("last(obs_ptr)-1 != length(y)"))
        return new{M,T}(model,y,x,xsum,nu,xpnu, nusum, nusumsq, obs_ptr,group_ptr)
    end
end

const ObservationGroupProduce = ObservationGroup{<:DataProduce}
const DataOrObsProduction = Union{ObservationProduce,DataProduce}
const AbstractDataStructureProduction = Union{ObservationProduce,DataProduce,ObservationGroupProduce}

# Common interfaces
#---------------------------

_xpnu( d::DataOrObsProduction) = d.xpnu
_nu(   d::DataOrObsProduction) = d.nu
_xsum( d::DataOrObsProduction) = d.xsum
_num_x(d::DataOrObsProduction) = size(_xsum(d),1)
_nusum(d::DataOrObsProduction) = d.nusum
_nusumsq(d::DataOrObsProduction) = d.nusumsq

# Data-specific interfaces
#---------------------------

obs_ptr(  d::DataProduce) = d.obs_ptr
group_ptr(d::DataProduce) = d.group_ptr

# Observation Group interfaces
#---------------------------

function Observation(d::DataProduce, j::Integer)
    rng  = obsrange(d,j)
    y    = view(_y(d), rng)
    nu   = view(_nu(d), rng)
    x    = view(_x(d), :, rng)
    xsum = view(_xsum(d), :, j)
    xpnu = view(_xpnu(d), :, j)
    nusum = getindex(_nusum(d), j)
    nusumsq = getindex(_nusumsq(d),j)
    return ObservationProduce(_model(d),y, x, xsum, nu, xpnu, nusum, nusumsq)
end

getindex(g::ObservationGroupProduce, k) = Observation(_data(g), getindex(grouprange(g), k))
Observation(g::ObservationGroupProduce, k) = getindex(g,k)

# Observation-specific interfaces
#---------------------------

function ==(o1::ObservationProduce, o2::ObservationProduce)
    _y(o1)       == _y(o2) &&
    _x(o1)       == _x(o2) &&
    _xsum(o1)    == _xsum(o2) &&
    _nu(o1)      == _nu(o2) &&
    _xpnu(o1)    == _xpnu(o2) &&
    _nusum(o1)   == _nusum(o2) &&
    _nusumsq(o1) == _nusumsq(o2)
end

function update_nu!(d::DataOrObsProduction, theta)
    length(theta) == _nparm(d) || throw(DimensionMismatch())
    _nu(d) .= _y(d) - _x(d)'*theta_produce_β(d,theta)
    for j in OneTo(_num_obs(d))
        obs = Observation(d, j)
        nu = _nu(obs)
        setindex!(_nusum(d),   sum(nu),    j)
        setindex!(_nusumsq(d), dot(nu,nu), j)
    end
    return nothing
end

function update_xsum!(obs::ObservationProduce)
    xsum = reshape(_xsum(obs), :, 1)
    sum!(xsum, _x(obs))
    return nothing
end

function update_xpnu!(obs::ObservationProduce)
    mul!(_xpnu(obs), _x(obs), _nu(obs))
    return nothing
end

update_xsum!(data::DataProduce) = update_over_obs(update_xsum!, data)
update_xpnu!(data::DataProduce) = update_over_obs(update_xpnu!, data)

function update!(d::DataProduce, theta)
    update_nu!(d, theta)
    update_xpnu!(d)
end

# Abstract data strucutres
#---------------------------

_nparm(d::AbstractDataStructureProduction) = _num_x(d)+3
idx_produce(d::AbstractDataStructureProduction) = OneTo(_nparm(d))
theta_produce(d, theta) = view(theta, idx_produce(d))

idx_produce_ψ() = 1
idx_produce_g() = 2
idx_produce_t() = 3
idx_produce_D() = 4
idx_produce_ψ(  d::Union{AbstractDataStructureProduction,ProductionModel}) =
    idx_produce_ψ()
idx_produce_g(  d::Union{AbstractDataStructureProduction,ProductionModel}) =
    idx_produce_g()
idx_produce_t(  d::Union{AbstractDataStructureProduction,ProductionModel}) =
    idx_produce_t()
idx_produce_D(  d::Union{AbstractDataStructureProduction,ProductionModel}) =
    idx_produce_D()
idx_produce_β(  d::AbstractDataStructureProduction) = 1 .+ (1:_num_x(d))
idx_produce_σ2η(d::AbstractDataStructureProduction) = 2 + _num_x(d)
idx_produce_σ2u(d::AbstractDataStructureProduction) = 3 + _num_x(d)

theta_produce_ψ(  d, theta) = theta[idx_produce_ψ(d)]
theta_produce_β(  d, theta) = view(theta, idx_produce_β(d))
theta_produce_σ2η(d, theta) = theta[idx_produce_σ2η(d)]
theta_produce_σ2u(d, theta) = theta[idx_produce_σ2u(d)]

theta_produce_β(  d::ProductionModel, theta) = view(theta, 2:length(theta)-2)
theta_produce_σ2η(d::ProductionModel, theta) = theta[end-1] # ACTUALLY ση
theta_produce_σ2u(d::ProductionModel, theta) = theta[end]   # ACTUALLY σu

function coefnames(d::AbstractDataStructureProduction)
    nms = Vector{String}(undef, _nparm(d))
    nms[idx_produce_ψ(d)]   = "\\alpha_\\psi"
    beta_idx = idx_produce_β(d) .- 1
    nms[idx_produce_β(d)]  .= ["\\gamma_{$i}" for i in beta_idx]
    nms[idx_produce_g(d)]   = "\\alpha_g"
    nms[idx_produce_σ2η(d)] = "\\sigma_\\eta"
    nms[idx_produce_σ2u(d)] = "\\sigma_u"
    return nms
end

# Dataset generator
#---------------------------

"""
    DataProduce(y, x, xsum, obsptr, grpptr)

Makes dataset and creats xsum, nu automatically
"""
function DataProduce(y::Vector{T}, x::Matrix{T}, obs_ptr::Vector, group_ptr::Vector) where {T}

    k,n = size(x)
    nwells = length(obs_ptr)-1

    xsum = Matrix{T}(undef, k, nwells)
    xpnu = similar(xsum)
    nu   = Vector{T}(undef, n)
    nusum = Vector{T}(undef, nwells)
    nusumsq = similar(nusum)

    data = DataProduce(ProductionModel(),y,x,xsum,nu,xpnu,nusum,nusumsq,obs_ptr,group_ptr)

    update_xsum!(data)

    return data
end

"""
    DataProduce(ngroups, maxwells, ntrange, theta)

Use `theta` to make random dataset with `ngroups` of wells that have
a random number of wells in `0:maxwells` that each have
a random draw of `ntrange` observations.
"""
function DataProduce(psi::Vector, maxwells::Int, ntrange::UnitRange, theta::Vector, args...)
    ngroups = length(psi)
    grouplens = vcat(collect(0:maxwells)..., sample(0:maxwells, ngroups-maxwells-1))
    ncoef = length(theta)-3

    return DataProduce(psi,grouplens,ntrange,theta, args...)
end

function DataProduce(psi::Vector, grouplens::Vector, ntrange::UnitRange, theta::Vector, ivars::Union{Number,Vector}=0)

    length(psi) == length(grouplens) || throw(DimensionMismatch())
    length(theta) > 3 || throw(DimensionMismatch())
    alphapsi = theta[1]
    beta = theta[2:end-2]
    sigeta, sigu = theta[end-1:end]

    ncoef = length(beta)

    # groups
    groupptr = 1 .+ cumsum(vcat(0, grouplens))
    nwells = sum(grouplens)

    us = randn(nwells)
    obslens = vcat(0, sample(ntrange, nwells))
    obsptr = 1 .+ cumsum(obslens)

    # observations
    nobs = last(obsptr)-1

    eta  = randn(nobs)
    x    = randn(ncoef,nobs)
    y    = similar(eta)

    data = DataProduce(y,x,obsptr,groupptr)

    if length(ivars) == length(psi)
        for (i,g) in enumerate(data)
            for (k,o) in enumerate(g)
                j = getindex(grouprange(g), k)
                xj = _x(o)
                xj[1,:] .= ivars[i]
            end
        end
    end

    y .= x'*beta .+ sigeta .* eta

    for (i,g) in enumerate(data)
        for (k,o) in enumerate(g)
            j = getindex(grouprange(g), k)
            y = _y(o) # if we don't do this, errors on julia v1.1.1
            y .+= sigu .* us[j] .+ alphapsi .* psi[i]
        end
    end

    update_xsum!(data)
    update_nu!(data, theta)

    return data
end

DataProduce(ngroups::Int, args...) = DataProduce(randn(ngroups), args...)


text:
function SCBQR!( A::SharedArray,
                 B::SparseMatrixCSC,
                 C::SharedArray,
                 M::Array )
  m,n = size(A)
  U, Z = tsqr!(A)
  U = constructQ!( U )

  blas_set_num_threads( nworkers() )

  # C := B*U
  mkl_cscsymm!( sdata(C), B, sdata(U) )

  # M := U'*C
  BLAS.gemm!( 'T', 'N', 1.0, U.s, C, 0.0, M )

  LAPACK.potrf!('U', M)

  # Q := U/M, R := M*Z
  BLAS.trsm!( 'R', 'U', 'N', 'N', 1.0, M, U )
  BLAS.trmm!( 'L', 'U', 'N', 'N', 1.0, M, Z )

  blas_set_num_threads( 1 )
  return Z
end

function CBQR!( A::SharedArray,
                B::SparseMatrixCSC,
                C::SharedArray,
                M::Array )
  m,n = size(A)

  blas_set_num_threads( nworkers() )
  # C := B*A
  mkl_cscsymm!( sdata(C), B, sdata(A) )

  # M := A'*C
  BLAS.gemm!( 'T', 'N', 1.0, A, C, 0.0, M )
  # Cholesky factorize M
  LAPACK.potrf!( 'U', M )
  # A := A/M
  BLAS.trsm!( 'R', 'U', 'N', 'N', 1.0, M, A )
  blas_set_num_threads( 1 )
  return triu(M)
end

function SCBQRT!( A::SharedArray,
                  B::SparseMatrixCSC,
                  C::SharedArray,
                  M::Array )
  m,n = size(A)
  Z = tsqr(A)

  blas_set_num_threads( nworkers() )

  BLAS.trsm!( 'R', 'U', 'N', 'N', 1.0, Z, A )

  mkl_cscsymm!( sdata(C), B, sdata(A) )

  BLAS.gemm!( 'T', 'N', 1.0, A, C, 0.0, M )
  LAPACK.potrf!( 'U', M )
  BLAS.trsm!( 'R', 'U', 'N', 'N', 1.0, M, A )
  BLAS.trmm!( 'L', 'U', 'N', 'N', 1.0, M, Z )

  blas_set_num_threads( 1 )
  return Z
end


text:
partial = false
include("lorenz.jl")
include("../extra/makie.jl")
using Makie, GLVisualize
using GeometryTypes, Colors
using Bridge: _viridis
skippoints = 1;
extra = 40
scene = Scene(resolution = (800, 800))
eyeposition = Float32[-37.2262, 65.8173, 37.4411]
sphere = Sphere(Point3f0(0,0,0), 1.0f0)
circle = Sphere(Point2f0(0,0), 1.0f0)
#RGB(Bridge._viridis[20]...)
maxviri = 200

#for i in indices(Paths)[1]
#    viri = _viridis[round.(Int,linspace(1,maxviri, length(Paths[i])))]
#    lines(Paths[i], linewidth = 0.1, color = map(x->RGBA(Float32.(x)..., 0.5f0), viri) )
#end
viri = _viridis[round.(Int,range(1, stop=maxviri, length=length(Xtrue)))]
lines(( Xtrue.yy), linewidth = 0.4, color = map(x->RGBA(Float32.(x)..., 1.0f0), viri[1:skippoints:end]) )
#lines(Xtrue.yy, linewidth = 0.2, color = :black )

viri = _viridis[round.(Int,range(1, stop=maxviri, length=length(Xmean)))]
#lines((@view Xmean[1:extra*skippoints:end]), linewidth = 0.2, color = map(x->RGBA(Float32.(x)..., 0.5f0), viri[1:extra*skippoints:end]) )
scatter( Xmean[1:extra*skippoints:end], marker = circle, markersize=0.2, color = map(x->RGBA(Float32.(x)..., 0.5f0), viri[1:extra*skippoints:end]) )

viri = _viridis[round.(Int,range(1, stop=maxviri, length=length(Xscal)))]
visualize_uncertainty(scene, (Xmean, Xrot, Xscal .* 1.f0), extra*skippoints; color = map(x->RGBA(Float32.(x)..., 0.05f0), viri[1:extra*skippoints:end]) )

ma = Float32[10,10,10]
axis(map(x -> UnitRange(0, round.(Int,x)), ma)..., showaxis = (true,true,true), showgrid = (false,false,false))
ma2 = ma .+ 2
for (x, c) in zip(ℝ{3}[(ma2[1], 0, 0), (0, ma2[2], 0),(0, 0, ma2[3]), (0,0,0)], ['x', 'y', 'z', '•'])
    scatter([x], marker = c, markersize = 1., color = :black)
end

center!(scene)
println(Makie.getscreen(scene).cameras[:perspective].view.value)

push!(Makie.getscreen(scene).cameras[:perspective].view,
    @SArray Float32[0.433338 0.901231 -3.7998f-7 1.95197; -0.237208 0.114057 0.96474 -20.4296; 0.869454 -0.418059 0.263205 -90.2712; 0.0 0.0 0.0 1.0]
)

Makie.save(joinpath("output", simname, "lorenz5n$simid.png"), scene);


text:
# NOTE
# Did a prior analysis for a version of repFAM where Z is
# a function of H, v. The results were underwhelming, and we couldn't
# achieve repulsiveness. Need to give up this idea.

import Pkg; Pkg.activate("../../")
include("HMC.jl")
using Distributions
using StatsBase

function grad_logprobH(H, j, k, phi)
  J, K = size(H)
  out = -H[j, k]
  for m in 1:K
    if m != k
      dmk = mean((H[:, k] - H[:, m]) .^ 2)
      tmp = zero(H[1])
      tmp += mean(H[:, k] - H[:, m]) / (exp(dmk / phi) - 1)
      out += tmp * 2 / phi
    end
  end
  return out
end

function grad_logprobH(H, phi)
  J, K = size(H)
  return [grad_logprobH(H, j, k, phi) for j in 1:J, k in 1:K]
end

"""
log1m(x) = log1p(-x) = log(1 - x)
"""
log1m(x) = log1p(-x)

function logprobH(H, phi)
  J, K = size(H)
  normal_kernel = -sum((H .^ 2)) / 2
  penalty = zero(H[1])

  for m in 1:(K - 1)
    for n in (m + 1):K
      d = mean((H[:, m] - H[:, n]) .^ 2)
      penalty += log1m(exp(-d / phi))
    end
  end

  return normal_kernel + penalty
end

struct State H end

function drawH(J, K, phi)
  if phi == 0
    randn(J, K)
  else
    # TODO
    0
  end
end

function drawH(n, J, K, phi)
  if phi == 0
    [randn(J, K) for _ in 1:n]
  else
    # TODO

  end
end

"""
NOTE:
Let H be a JxK continuous matrix, with H_{jk} \\in \\mathbb{R}.
Let Z be a JxK binary matrix.
Let v be a K-dimensional continuous vector, bounded within the unit interval.

Model:
Z_{jk} = 1(v_{k} > \\Phi(H_{jk}))
v_k | \\alpha ~ Beta(\\alpha/K, 1)
p(H) \\propto \\prod_{j,k} exp(-H_{jk}^2/2) *
              \\prod{k\\ne k'} 1 - \\exp(-d_{k,k'} / \\phi)
"""
function drawZ(J, K, alpha, phi; stickbreak=false)
  if stickbreak
    v = cumprod(rand(Beta(alpha, 1), 1, K), dims=2)
  else
    v = rand(Beta(alpha / K, 1), 1, K)
  end
  H = drawH(J, K, phi)
  return v .> cdf.(Normal(0, 1), H)
end

function drawH(n, J, K, phi; num_leapfrog_steps=2^6, eps=.01, burn=0)
  lp(H) = logprobH(H, phi)
  grad_lp(H) = grad_logprobH(H, phi)

  H = randn(J, K)
  for _ in 1:burn
    H, _ = HMC.hmc_update(H, lp, grad_lp, num_leapfrog_steps, eps)
  end

  Hs = [zeros(J, K) for _ in 1:n]
  lpHs = zeros(n)

  for i in 1:n
    H, lpH = HMC.hmc_update(H, lp, grad_lp, num_leapfrog_steps, eps)
    Hs[i] .= copy(H)
    lpHs[i] = lpH
  end

  return Hs, lpHs
end

function drawZ(N, J, K, alpha, phi;
               stickbreak=false, num_leapfrog_steps=2^6, eps=.01, burn=0)
  if stickbreak
    vs = [cumprod(rand(Beta(alpha, 1), 1, K), dims=2) for _ in 1:N]
  else
    vs = [rand(Beta(alpha / K, 1), 1, K) for _ in 1:N]
  end

  Hs, lpH = drawH(N, J, K, phi,
                  num_leapfrog_steps=num_leapfrog_steps, eps=eps, burn=burn)

  return [vs[i] .> cdf.(Normal(0, 1), Hs[i]) for i in 1:N]
end

# Simulate
N, alpha, phi, J, K, burn = (10000, 0.5, 100.0, 2, 2, 100)
@time Zs = drawZ(N, J, K, alpha, phi, stickbreak=true, burn=burn)
Zcounts = countmap(Zs)
sort(collect(Zcounts), by=x -> -x.second)


text:
isabaquskeyword(l) = startswith(l, "*")

function join_multiline_elementdata(element_data::Vector{<:AbstractString})
    fixed_element_data = copy(element_data)
    i = 0
    i_fixed = 0
    nrows = length(element_data)
    while i < nrows
        i += 1
        length(element_data[i])==0 && continue
        i_fixed += 1
        fixed_element_data[i_fixed] = element_data[i]
        while endswith(fixed_element_data[i_fixed], ',') && i < nrows
            i += 1
            fixed_element_data[i_fixed] = fixed_element_data[i_fixed]*element_data[i]
        end
    end
    return fixed_element_data[1:i_fixed]
end

function read_abaqus_nodes!(f, node_numbers::Vector{Int}, coord_vec::Vector{Float64})
    local coords
    node_data = readlinesuntil(f; stopsign='*')
    for nodeline in node_data
        node = split(nodeline, ',', keepempty = false)
        length(node) == 0 && continue
        push!(node_numbers, parse(Int, node[1]))
        coords = parse.(Float64, node[2:end])
        append!(coord_vec, coords)
    end
    return length(coords)
end

function read_abaqus_elements!(f, topology_vectors, element_number_vectors, element_type::AbstractString, element_set="", element_sets=nothing)
    if !haskey(topology_vectors, element_type)
        topology_vectors[element_type] = Int[]
        element_number_vectors[element_type] = Int[]
    end
    topology_vec = topology_vectors[element_type]
    element_numbers = element_number_vectors[element_type]
    element_numbers_new = Int[]
    element_data_raw = readlinesuntil(f; stopsign='*')
    element_data = join_multiline_elementdata(element_data_raw)
    for elementline in element_data
        element = split(elementline, ',', keepempty = false)
        length(element) == 0 && continue
        n = parse(Int, element[1])
        push!(element_numbers_new, n)
        vertices = [parse(Int, element[i]) for i in 2:length(element)]
        append!(topology_vec, vertices)
    end
    append!(element_numbers, element_numbers_new)
    if element_set != ""
        element_sets[element_set] = copy(element_numbers_new)
    end
end

function read_abaqus_set!(f, sets, setname::AbstractString)
    if endswith(setname, "generate")
        splitted_line = split(strip(eat_line(f)), ",", keepempty = false)
        start, stop, step = [parse(Int, x) for x in splitted_line]
        indices = collect(start:step:stop)
        setname = split(setname, [','])[1]
    else
        data = readlinesuntil(f; stopsign='*')
        indices = Int[]
        for line in data
            indices_str = split(line, ',', keepempty = false)
            for v in indices_str
                push!(indices, parse(Int, v))
            end
        end
    end
    sets[setname] = indices
end

function read_mesh(filename, ::AbaqusMeshFormat)
    dim = 0
    node_numbers = Int[]
    coord_vec = Float64[]

    topology_vectors = Dict{String, Vector{Int}}()
    element_number_vectors = Dict{String, Vector{Int}}()

    nodesets = Dict{String, Vector{Int}}()
    elementsets = Dict{String, Vector{Int}}()
    part_counter = 0
    instance_counter = 0

    open(filename) do f
        while !eof(f)
            header = eat_line(f)
            if header == ""
                continue
            end
            DEBUG_PARSE && println("H: $header")
            if startswith(lowercase(header), "*node")
                DEBUG_PARSE && println("Reading nodes")
                read_dim = read_abaqus_nodes!(f, node_numbers, coord_vec)
                dim == 0 && (dim = read_dim)  # Set dim if not yet set
                read_dim != dim && throw(DimensionMismatch("Not allowed to mix nodes in different dimensions"))
            elseif startswith(lowercase(header), "*element")
                if ((m = match(r"\*Element, type=(.*), ELSET=(.*)"i, header)) !== nothing)
                    DEBUG_PARSE && println("Reading elements with elset")
                    read_abaqus_elements!(f, topology_vectors, element_number_vectors,  m.captures[1], m.captures[2], elementsets)
                elseif ((m = match(r"\*Element, type=(.*)"i, header)) !== nothing)
                    DEBUG_PARSE && println("Reading elements without elset")
                    read_abaqus_elements!(f, topology_vectors, element_number_vectors,  m.captures[1])
                end
            elseif ((m = match(r"\*Elset, elset=(.*)"i, header)) !== nothing)
                DEBUG_PARSE && println("Reading elementset")
                read_abaqus_set!(f, elementsets, m.captures[1])
            elseif ((m = match(r"\*Nset, nset=(.*)"i, header)) !== nothing)
                DEBUG_PARSE && println("Reading nodeset")
                read_abaqus_set!(f, nodesets, m.captures[1])
            elseif startswith(lowercase(header), "*part")
                DEBUG_PARSE && println("Increment part counter")
                part_counter += 1
            elseif startswith(lowercase(header), "*instance")
                DEBUG_PARSE && println("Increment instance counter")
                instance_counter += 1
                discardlinesuntil(f, stopsign='*')  # Instances contain translations, or start with *Node if independent mesh
            elseif isabaquskeyword(header)          # Ignore unused keywords
                DEBUG_PARSE && println("Discarding keyword content")
                discardlinesuntil(f, stopsign='*')
            else
                if eof(f)
                    break
                else
                    throw(InvalidFileContent("Unknown header, \"$header\", in file \"$filename\""))
                end
            end
        end

        if part_counter > 1 || instance_counter > 1
            msg = "Multiple parts or instances are not supported\n"
            msg *= "Tip: If you want a single grid, merge parts and differentiated by Abaqus sets\n"
            msg *= "     If you want multiple grids, split into multiple input files"
            throw(InvalidFileContent(msg))
        end
    end

    elements = Dict{String, RawElements}()
    for element_type in keys(topology_vectors)
        topology_vec = topology_vectors[element_type]
        element_numbers = element_number_vectors[element_type]
        n_elements = length(element_numbers)
        topology_matrix = reshape(topology_vec, length(topology_vec) ÷ n_elements, n_elements)
        elements[element_type] = RawElements(numbers=element_numbers, topology=topology_matrix)
    end
    nodes = RawNodes(numbers=node_numbers, coordinates=reshape(coord_vec, dim, length(coord_vec) ÷ dim))
    return RawMesh(elements=elements, nodes=nodes, nodesets=nodesets, elementsets=elementsets)
end