### A Pluto.jl notebook ###
# v0.19.4

using Markdown
using InteractiveUtils

# ╔═╡ 4458903f-4717-4603-a707-4d2fd587470b
using Pkg, DrWatson

# ╔═╡ d577b8c8-3670-497a-a6fe-41208a8e8501
begin
	using Turing
	using DataFrames
	using CSV
	using Random
	using Dagitty
	using Distributions
	using StatisticalRethinking
	using StatisticalRethinking: link
	using StatisticalRethinkingPlots
	using StatsPlots
	using StatsBase
	using Logging
	using LinearAlgebra
end

# ╔═╡ 95965ab2-f250-479f-9d5d-e478dba1fe35
html"""
<style>
	main {
		margin: 0 auto;
		max-width: 2000px;
    	padding-left: max(160px, 10%);
    	padding-right: max(160px, 10%);
	}
</style>
"""

# ╔═╡ 90028541-7308-476f-b51b-850cd6ad39c4
begin
	default(label=false);
	Logging.disable_logging(Logging.Warn)
end;

# ╔═╡ 1217e4ab-8e97-4b73-9493-a58c7d8165fe
md" ## 14.1 Varying slopes by construction."

# ╔═╡ 100c3470-b7e4-4890-9347-851b78f5202f
md" #### Code 14.1 - 14.4"

# ╔═╡ 464ddfd5-d06b-4615-bd23-e63e03a29f1e
md"

!!! note

Julia has similar `column-first` matix order."

# ╔═╡ fe81bd6a-c7bf-437d-8ca6-f21f9b45b41f
reshape(1:4, (2,2))

# ╔═╡ b6c8f7af-8e39-4792-a62c-88a41876345d
md" #### Code 14.5 - 14.8"

# ╔═╡ 8ee2eec3-3214-48d1-8604-a54ba1a67baf
let
	a = 3.5    # average morning wait time
	b = -1     # average difference afternoon wait time
	σ_a = 1    # std dev in intercepts
	σ_b = 0.5  # std dev in slopes
	ρ = -0.7;  # correlation between intercepts and slopes
	
	global μ = [a, b]
	cov_ab = σ_a * σ_b * ρ
	global Σ₂ = [[σ_a^2, cov_ab] [cov_ab, σ_b^2]]
	sigmas = [σ_a, σ_b]
	Ρ = [[1, ρ] [ρ, 1]]
	
	global Σ₃ = Diagonal(sigmas) * Ρ * Diagonal(sigmas)
	N_cafes = 20
	Random.seed!(5)
	vary_effect = rand(MvNormal(μ, Σ₃), N_cafes)
	global a_cafe = vary_effect[1,:]
	global b_cafe = vary_effect[2,:];
end

# ╔═╡ 573253a5-10d4-458e-9451-89c763658810
md" #### Code 14.9"

# ╔═╡ fa9dff6f-3182-4093-bbfd-8deea404eab0
let
	p = scatter(a_cafe, b_cafe, xlab="intercepts (a_cafe)", ylab="slopes (b_cafe)")
	
	d = acos(Σ₂[1,2])
	chi = Chisq(2)
	
	for l ∈ (0.1, 0.3, 0.5, 0.8, 0.99)
	    scale = sqrt(quantile(chi, l))
	    xₜ(t) = scale*Σ₂[1,1]*cos(t + d/2) + μ[1]
	    yₜ(t) = scale*Σ₂[2,2]*cos(t - d/2) + μ[2]
	
	    plot!(xₜ, yₜ, 0, 2π, c=:black, alpha=0.3)
	end
	p
end

# ╔═╡ 2367f3cf-c568-4f6c-82c6-b7ae42408404
md" #### Code 14.10"

# ╔═╡ 8185285a-1640-45e9-8c80-b17b6c960804
let
	Random.seed!(1)
	N_cafes = 20
	N_visits = 10
	
	afternoon = repeat(0:1, N_visits*N_cafes ÷ 2)
	cafe_id = repeat(1:N_cafes, inner=N_visits)
	μ = a_cafe[cafe_id] + b_cafe[cafe_id] .* afternoon
	σ = 0.5
	wait = rand.(Normal.(μ, σ))
	global cafes = DataFrame(cafe=cafe_id, afternoon=afternoon, wait=wait);
end

# ╔═╡ 40634f53-8104-4791-877c-2d498cab9570
md" #### Code 14.11"

# ╔═╡ 885a0261-3541-4389-beb7-231c77e2dfcc
let
	R = rand(LKJ(2, 2), 10^4);
	density(getindex.(R, 2), xlab="Correlation")
end

# ╔═╡ 6837fff8-0c29-4ba1-9b3b-b21c23d861eb
md" #### Code 14.12"

# ╔═╡ 1f30d601-4e00-44dd-a6ab-363c431ca875
@model function m14_1(cafe, afternoon, wait)
    a ~ Normal(5, 2)
    b ~ Normal(-1, 0.5)
    σ_cafe ~ filldist(Exponential(), 2)
    Rho ~ LKJ(2, 2)
    # build sigma matrix manually, to avoid numerical errors
#     (σ₁, σ₂) = σ_cafe
#     sc = [[σ₁^2, σ₁*σ₂] [σ₁*σ₂, σ₂^2]]
#     Σ = Rho .* sc
    # the same as above, but shorter and generic
    Σ = (σ_cafe .* σ_cafe') .* Rho
    ab ~ filldist(MvNormal([a,b], Σ), 20)
    a = ab[1,cafe]
    b = ab[2,cafe]
    μ = @. a + b * afternoon
    σ ~ Exponential()
    for i ∈ eachindex(wait)
        wait[i] ~ Normal(μ[i], σ)
    end
end

# ╔═╡ de06a783-c2ff-4f45-8a1e-02977ad31e26
begin
	Random.seed!(1)
	m14_1_ch = sample(m14_1(cafes.cafe, cafes.afternoon, cafes.wait), NUTS(), 1000)
	m14_1_df = DataFrame(m14_1_ch);
end

# ╔═╡ 30be727e-86e6-41cf-be58-e0b1ffb372c2
md" #### Code 14.13"

# ╔═╡ 5ca07e4a-bf45-4e3c-9a5b-3b9b7af38020
let
	density(m14_1_df."Rho[1,2]", lab="posterior", lw=2)
	R = rand(LKJ(2, 2), 10^4);
	density!(getindex.(R, 2), lab="prior", ls=:dash, lw=2)
	plot!(xlab="correlation", ylab="Density")
end

# ╔═╡ f95ec79a-0263-46e4-b82e-a274cb7ee7fb
md" #### Code 14.14"

# ╔═╡ 81f57cdb-36f8-43bb-86a5-19bac5cd88b1
md"

!!! note

Plot differs from presented in the book due to different seed in data generation."

# ╔═╡ 78fe51f6-beea-4155-905d-2d5e6e7d66d7
let
	N_cafes = 20
	gb = groupby(cafes[cafes.afternoon .== 0,:], :cafe)
	global a1 = combine(gb, :wait => mean).wait_mean
	
	gb = groupby(cafes[cafes.afternoon .== 1,:], :cafe)
	global b1 = combine(gb, :wait => mean).wait_mean .- a1
	
	global a2 = [mean(m14_1_df[:, "ab[1,$i]"]) for i ∈ 1:N_cafes]
	global b2 = [mean(m14_1_df[:, "ab[2,$i]"]) for i ∈ 1:N_cafes]
	
	xlim = extrema(a1) .+ (-0.1, 0.1)
	ylim = extrema(b1) .+ (-0.1, 0.1)
	
	global p_cafe = scatter(a1, b1, xlab="intercept", ylab="slope", xlim=xlim, ylim=ylim)
	
	scatter!(a2, b2, mc=:white)
	
	for (x1,y1,x2,y2) ∈ zip(a1, b1, a2, b2)
	    plot!([x1,x2], [y1,y2], c=:black)
	end
	p_cafe
end

# ╔═╡ 4ea3a429-e457-48a1-a66a-ea66ff21d22c
md" #### Code 14.15"

# ╔═╡ 8bb5afba-3f59-4776-9a7b-8df9fed58a90
let
	# posterior mean
	ρ = mean(m14_1_df."Rho[1,2]")
	μ_a = mean(m14_1_df.a)
	μ_b = mean(m14_1_df.b)
	σ₁ = mean(m14_1_df."σ_cafe[1]")
	σ₂ = mean(m14_1_df."σ_cafe[2]")
	
	# draw ellipses
	dt = acos(ρ*σ₁*σ₂)
	chi = Chisq(2)
	
	for l ∈ (0.1, 0.3, 0.5, 0.8, 0.99)
	    scale = sqrt(quantile(chi, l))
	    xₜ(t) = scale*σ₁^2*cos(t + dt/2) + μ_a
	    yₜ(t) = scale*σ₂^2*cos(t - dt/2) + μ_b
	
	    plot!(xₜ, yₜ, 0, 2π, c=:black, alpha=0.3)
	end
	
	p_cafe
end

# ╔═╡ 5188efaa-8a5e-4fac-9e7f-bf048079ab9c
md" #### Code 14.16"

# ╔═╡ 23810d4f-1dd6-4c16-bf71-231b8b4b726d
let
	wait_morning_1 = a1
	wait_afternoon_1 = a1 .+ b1
	wait_morning_2 = a2
	wait_afternoon_2 = a2 .+ b2
	
	global p = scatter(wait_morning_1, wait_afternoon_1, xlab="morning wait", ylab="afternoon wait")
	scatter!(wait_morning_2, wait_afternoon_2, mc=:white)
	
	plot!(x -> x, s=:dash)
	
	for (x1,y1,x2,y2) ∈ zip(wait_morning_1, wait_afternoon_1, wait_morning_2, wait_afternoon_2)
	    plot!([x1,x2], [y1,y2], c=:black)
	end
	p
end

# ╔═╡ 91780708-0829-4beb-8144-7fc5b7e76b3f
md" #### Code 14.17"

# ╔═╡ cdeba577-a184-4bb5-97a9-6acf3ff516a3
let
	Random.seed!(1)
	
	# posterior mean
	ρ = mean(m14_1_df."Rho[1,2]")
	μ_a = mean(m14_1_df.a)
	μ_b = mean(m14_1_df.b)
	σ₁ = mean(m14_1_df."σ_cafe[1]")
	σ₂ = mean(m14_1_df."σ_cafe[2]")

	Σ = [[σ₁^2, σ₁*σ₂*ρ] [σ₁*σ₂*ρ, σ₂^2]]
	μ = [μ_a, μ_b]
	v = rand(MvNormal(μ, Σ), 10^4)
	v[2,:] += v[1,:]
	Σ₂ = cov(v')
	μ₂ = [μ_a, μ_a+μ_b]
	
	# draw ellipses
	dt = acos(Σ₂[1,2])
	chi = Chisq(2)
	
	for l ∈ (0.1, 0.3, 0.5, 0.8, 0.99)
	    scale = sqrt(quantile(chi, l))
	    xₜ(t) = scale*Σ₂[1,1]*cos(t + dt/2) + μ₂[1]
	    yₜ(t) = scale*Σ₂[2,2]*cos(t - dt/2) + μ₂[2]
	
	    plot!(xₜ, yₜ, 0, 2π, c=:black, alpha=0.3)
	end
	
	p
end

# ╔═╡ e049f64c-02e0-4087-b341-eaf437c5ba49
md" ## 14.2 Advanced varying slopes."

# ╔═╡ 687aec56-682c-4153-ac35-58926c03ea26
md" #### Code 14.18"

# ╔═╡ 0c918f86-e896-4b19-8cf8-a77203c3a61b
begin
	chimpanzees = CSV.read(sr_datadir("chimpanzees.csv"), DataFrame)
	chimpanzees.treatment = 1 .+ chimpanzees.prosoc_left .+ 2*chimpanzees.condition;
	chimpanzees.block_id = chimpanzees.block;
end;

# ╔═╡ fee0f70c-9aa5-4b60-a285-6923fedbd06c
@model function m14_2(L, tid, actor, block_id)
    tid_len = length(levels(tid))
    act_len = length(levels(actor))
    blk_len = length(levels(block_id))
    g ~ filldist(Normal(), tid_len)

    σ_actor ~ filldist(Exponential(), tid_len)
    ρ_actor ~ LKJ(tid_len, 2)
    Σ_actor = (σ_actor .* σ_actor') .* ρ_actor
    alpha ~ filldist(MvNormal(zeros(tid_len), Σ_actor), act_len)

    σ_block ~ filldist(Exponential(), tid_len)
    ρ_block ~ LKJ(tid_len, 2)
    Σ_block = (σ_block .* σ_block') .* ρ_block
    beta ~ filldist(MvNormal(zeros(tid_len), Σ_block), blk_len)
    
    for i ∈ eachindex(L)
        p = logistic(g[tid[i]] + alpha[tid[i], actor[i]] + beta[tid[i], block_id[i]])
        L[i] ~ Bernoulli(p)
    end
end

# ╔═╡ 57050894-2fcb-48e0-bd41-14502da1b5ae
begin
	Random.seed!(123)
	m14_2_ch = sample(m14_2(chimpanzees.pulled_left, chimpanzees.treatment, chimpanzees.actor, chimpanzees.block_id),
		HMC(0.01, 10), 1000);
	m14_2_df = DataFrame(m14_2_ch);
end

# ╔═╡ 2a1dd0cf-5a09-43bd-b7bf-5c93bea3bf3b
md" #### Code 14.19"

# ╔═╡ d15e5041-6021-483e-b059-7170077c2ea6
@model function m14_3(L, tid, actor, block_id)
    tid_len = length(levels(tid))
    act_len = length(levels(actor))
    blk_len = length(levels(block_id))
    g ~ filldist(Normal(), tid_len)

    σ_actor ~ filldist(Exponential(), tid_len)
    # LKJCholesky is not usable in Turing: https://github.com/TuringLang/Turing.jl/issues/1629
    ρ_actor ~ LKJ(tid_len, 2)    
    ρ_actor_L = cholesky(Symmetric(ρ_actor)).L
    z_actor ~ filldist(MvNormal(zeros(tid_len), 1), act_len)
    alpha = (σ_actor .* ρ_actor_L) * z_actor

    σ_block ~ filldist(Exponential(), tid_len)
    ρ_block ~ LKJ(tid_len, 2)
    ρ_block_L = cholesky(Symmetric(ρ_block)).L        
    z_block ~ filldist(MvNormal(zeros(tid_len), 1), blk_len)
    beta = (σ_block .* ρ_block_L) * z_block

    for i ∈ eachindex(L)
        p = logistic(g[tid[i]] + alpha[tid[i], actor[i]] + beta[tid[i], block_id[i]])
        L[i] ~ Bernoulli(p)
    end
end

# ╔═╡ 425eea72-221d-4990-90f2-a6654f4e98e1
md"

!!! note

Hm, this is less stable and slower than m14_2...
So if you know how to improve it - PR or open the issue in the repo"

# ╔═╡ ccc7d18c-08ed-41a7-a556-26030a19d6c5
begin
	Random.seed!(123)
	m14_3_ch = sample(m14_3(chimpanzees.pulled_left, chimpanzees.treatment, chimpanzees.actor, chimpanzees.block_id), 
    	HMC(0.01, 10), 1000)
	CHNS(m14_2_ch)
end

# ╔═╡ 6b73a8a5-c542-4a10-8cf1-0a7e40c3cc98
md" #### Code 14.20"

# ╔═╡ bc41a9ab-c960-4d17-9782-f01721337aea
let
	t = DataFrame(ess_rhat(m14_2_ch));
	ess_2 = t.ess[occursin.(r"σ|ρ", string.(t.parameters))]
	ess_2 = filter(v -> !isnan(v), ess_2);
	t = DataFrame(ess_rhat(m14_3_ch));
	ess_3 = t.ess[occursin.(r"σ|ρ", string.(t.parameters))]
	ess_3 = filter(v -> !isnan(v), ess_3);
	
	bounds = extrema([ess_2; ess_3]) .+ (-20, 20)
	scatter(ess_2, ess_3, xlim=bounds, ylim=bounds, xlab="centered (default)", ylab="non-centered (cholesky)")
	plot!(identity)
end

# ╔═╡ 40ec9daa-913e-4b2c-a0aa-3e70a2de7c71
md" #### Code 14.21"

# ╔═╡ b938e63c-29b1-4e49-90af-f9b2ab2e5bdd
begin
	m14_3_df = DataFrame(m14_3_ch)
	PRECIS(m14_3_df[:, r"σ"])
end

# ╔═╡ e5428608-cfc2-4fb0-873d-9a4944fb27f6
md" #### Code 14.22"

# ╔═╡ 0d6baf1d-2e2a-4742-944a-072bbd24b628
md"

!!! note

The results for both models 2 and 3 are weird and mismatch with the book. So, something is wrong here.
Put below both link functions for experimentations.

Plot is from model 2, because model 3 is totally off."

# ╔═╡ ef730308-7bf8-489a-9ab5-a869efe6083a
let
	gd = groupby(chimpanzees, [:actor, :treatment])
	c = combine(gd, :pulled_left => mean => :val)
	global pl = unstack(c, :actor, :treatment, :val);
end

# ╔═╡ 1c4b4cb8-12c0-4fb3-8523-062c7028f746
l_fun = (r, (ai, ti)) -> begin
    bi = 5
    g = get(r, "g[$ti]", missing)
    
    σ_actor = get(r, "σ_actor[$ti]", missing)
    ρ_actor = reshape(collect(r[r"ρ_actor"]), (4, 4))
    ρ_actor_L = cholesky(Symmetric(ρ_actor)).L
    z_actor = reshape(collect(r[r"z_actor"]), (4, 7))
    alpha = (σ_actor .* ρ_actor_L) * z_actor
    a = alpha[ti, ai]
    
    σ_block = get(r, "σ_block[$ti]", missing)
    ρ_block = reshape(collect(r[r"ρ_block"]), (4, 4))
    ρ_block_L = cholesky(Symmetric(ρ_block)).L
    z_block = reshape(collect(r[r"z_block"]), (4, 6))
    beta = (σ_block .* ρ_block_L) * z_block
    b = beta[ti, bi]
    
    logistic(g + a + b)
end

# ╔═╡ 9610477f-8311-4cbf-8544-b9f4836926d6
#p_post = link(m14_3_df, l_fun, Iterators.product(1:7, 1:4))

l_fun2 = (r, (ai, ti)) -> begin
    bi = 5
    g = get(r, "g[$ti]", missing)
    a = get(r, "alpha[$ti,$ai]", missing)
    b = get(r, "beta[$ti,$bi]", missing)
    logistic(g + a + b)
end

# ╔═╡ e5216885-c156-4454-ac96-eed454435695
p_post = link(m14_2_df, l_fun2, Iterators.product(1:7, 1:4))

# ╔═╡ 6e47526a-310a-4a3e-aab5-0fe71c6c7814
let
	p_μ = map(mean, p_post)
	p_ci = map(PI, p_post);
	rel_ci = map(idx -> (p_μ[idx]-p_ci[idx][1], p_ci[idx][2]-p_μ[idx]), CartesianIndices(p_ci));
	
	n_names = ["R/N", "L/N", "R/P", "L/P"]
	p = plot(ylims=(0, 1.1), ylab="proportion left lever", showaxis=:y, xticks=false)
	hline!([0.5], c=:gray, s=:dash)
	
	# raw data
	for actor in 1:7
	    ofs = (actor-1)*4
	    actor > 1 && vline!([ofs+0.5], c=:gray)
	    plot!([ofs+1,ofs+3], collect(pl[actor,["1","3"]]), lw=2, m=:o, c=:black)
	    plot!([ofs+2,ofs+4], collect(pl[actor,["2","4"]]), lw=2, m=:o, c=:black)
	    anns = [
	        (ofs+idx, pl[actor,string(idx)]+.04, (name, 8))
	        for (idx,name) ∈ enumerate(n_names)
	    ]
	    actor != 2 && annotate!(anns)
	end
	
	annotate!([
	    (2.5 + (idx-1)*4, 1.1, ("actor $idx", 8))
	    for idx ∈ 1:7
	])
	
	# posterior predictions
	for actor in 1:7
	    ofs = (actor-1)*4
	    actor > 1 && vline!([ofs+0.5], c=:gray)
	    err = [rel_ci[actor,1], rel_ci[actor,3]]
	    plot!([ofs+1,ofs+3], collect(p_μ[actor,[1,3]]), err=err, lw=2, m=:o, c=:blue)
	    err = [rel_ci[actor,2], rel_ci[actor,4]]    
	    plot!([ofs+2,ofs+4], collect(p_μ[actor,[2,4]]), err=err, lw=2, m=:o, c=:blue)
	end
	
	p
end

# ╔═╡ 944c59b8-ecf6-4ec3-9e81-7ffb8692db36
md" ## 14.3 Instruments and causal designs."

# ╔═╡ 233cd90e-463d-49fb-9a54-34e2750c2a8c
md" #### Code 14.23"

# ╔═╡ b28587b9-5e60-42b0-9874-d47b3e03b97c
let
	Random.seed!(73)
	N = 500
	U_sim = rand(Normal(), N)
	Q_sim = rand(1:4, N)
	E_sim = [rand(Normal(μ)) for μ ∈ U_sim .+ Q_sim]
	W_sim = [rand(Normal(μ)) for μ ∈ U_sim .+ 0*Q_sim]
	
	global dat_sim1 = DataFrame(
	    W=standardize(ZScoreTransform, W_sim),
	    E=standardize(ZScoreTransform, E_sim),
	    Q=standardize(ZScoreTransform, float.(Q_sim)),
	)
end

# ╔═╡ 4fb1f19d-2802-4a0f-bb35-1e21c0be68f3
md" #### Code 14.24"

# ╔═╡ aad09fb4-1fee-454f-bdad-65b2a93255ca
@model function m14_4(W, E)
    σ ~ Exponential()
    aW ~ Normal(0, 0.2)
    bEW ~ Normal(0, 0.5)
    μ = @. aW + bEW * E
    W ~ MvNormal(μ, σ)
end

# ╔═╡ 0d451930-833e-4050-b2f9-d5f997fb0098
begin
	m14_4_ch = sample(m14_4(dat_sim1.W, dat_sim1.E),
	    NUTS(), 1000)
	m14_4_df = DataFrame(m14_4_ch)
	PRECIS(m14_4_df)
end

# ╔═╡ 3878adef-0d96-4e73-ab37-4e761e01e0ac
md" #### Code 14.25"

# ╔═╡ 500fb09f-f952-46a0-8d63-98279e630882
@model function m14_5(W, E, Q)
    σ ~ Exponential()
    aW ~ Normal(0, 0.2)
    bEW ~ Normal(0, 0.5)
    bQW ~ Normal(0, 0.5)
    μ = @. aW + bEW * E + bQW * Q
    W ~ MvNormal(μ, σ)
end

# ╔═╡ 95d072b9-5940-49ce-97a8-8dde13c25939
begin
	m14_5_ch = sample(m14_5(dat_sim1.W, dat_sim1.E, dat_sim1.Q),
	    NUTS(), 1000)
	m14_5_df = DataFrame(m14_5_ch)
	PRECIS(m14_5_df)
end

# ╔═╡ 1f3d5631-8261-4c3b-8e34-761d23eb5e2e
md" #### Code 14.26"

# ╔═╡ a856d989-5fb6-4148-ac7d-2ce52952c1a3
@model function m14_6(W, E, Q, WE)
    σ ~ filldist(Exponential(), 2)
    ρ ~ LKJ(2, 2)
    aW ~ Normal(0, 0.2)
    aE ~ Normal(0, 0.2)
    bEW ~ Normal(0, 0.5)
    bQE ~ Normal(0, 0.5)
    μW = @. aW + bEW*E
    μE = @. aW + bQE*Q
    Σ = (σ .* σ') .* ρ
    for i ∈ eachindex(WE)
        WE[i] ~ MvNormal([μW[i], μE[i]], Σ)
    end
end

# ╔═╡ 9a7ebb96-5ce1-4093-8c85-9522edebab0e
begin
	Random.seed!(1)
	# need to combine W and E here (Turing vars limitation)
	WE = [[w,e] for (w,e) ∈ zip(dat_sim1.W, dat_sim1.E)]
	m14_6_ch = sample(m14_6(dat_sim1.W, dat_sim1.E, dat_sim1.Q, WE), NUTS(200, 0.65, init_ϵ=0.003), 1000)
	m14_6_df = DataFrame(m14_6_ch);
end

# ╔═╡ 48d158ed-a25f-4ebe-8863-6c92071c251c
let
	# Drop cols with zero variance
	df = m14_6_df[:, Not("ρ[1,1]")][:, Not("ρ[2,2]")]
	PRECIS(df)
end

# ╔═╡ 199ae6d5-7306-4802-bd18-4232fdb98f5f
md" #### Code 14.28"

# ╔═╡ aee19854-5c3d-4a9e-8639-91843800d1b6
let
	Random.seed!(73)
	
	N = 500
	U_sim = rand(Normal(), N)
	Q_sim = rand(1:4, N)
	E_sim = [rand(Normal(μ)) for μ ∈ U_sim .+ Q_sim]
	W_sim = [rand(Normal(μ)) for μ ∈ -U_sim .+ 0.2*Q_sim]
	
	global dat_sim2 = DataFrame(
	    W=standardize(ZScoreTransform, W_sim),
	    E=standardize(ZScoreTransform, E_sim),
	    Q=standardize(ZScoreTransform, float.(Q_sim)),
	);
end

# ╔═╡ e01fa7a9-16ac-498e-97d3-8c9fe1255f43
md" #### Code 14.29"

# ╔═╡ 48fe8dff-dc91-4996-bfe7-911d2a09b4c8
md"

!!! note

Not implemented in dagitty.jl yet."

# ╔═╡ aef2347f-dea0-4bbb-864c-c7d0d09814c6
let
	g = DAG(:Q => :E, :U => :E, :E => :W, :E => :W)
end

# ╔═╡ 011c2852-91b3-4745-b453-e0ffcdba7f23
md" ## 14.4 Social relations as correlated varying effects."

# ╔═╡ 6916ba32-8ebc-4aa7-adf7-f6717fde60e2
md" #### Code 14.30"

# ╔═╡ afaf9be1-a557-4b73-9279-f9cf12525958
begin
	kl_dyads = CSV.read(sr_datadir("KosterLeckie.csv"), DataFrame)
	describe(kl_dyads)
end

# ╔═╡ 1c03fd5e-0c6a-4118-b11a-0f4d2392f923
md" #### Code 14.31"

# ╔═╡ 1cd43a15-d361-4e4a-84e2-f1464659a654
# +
kl_data = (
    N = nrow(kl_dyads), 
    N_households = maximum(kl_dyads.hidB),
    did = kl_dyads.did,
    hidA = kl_dyads.hidA,
    hidB = kl_dyads.hidB,
    giftsAB = kl_dyads.giftsAB,
    giftsBA = kl_dyads.giftsBA,
)

# ╔═╡ 2be10e8e-9a44-4b0b-bd81-7e4cdc999afc
@model function m14_7(N, N_households, hidA, hidB, did, giftsAB, giftsBA)
    a ~ Normal()
    ρ_gr ~ LKJ(2, 4)
    σ_gr ~ filldist(Exponential(), 2)
    Σ = (σ_gr .* σ_gr') .* ρ_gr
    gr ~ filldist(MvNormal(Σ), N_households)
    
    # dyad effects (use 2 z values)
    z₁ ~ filldist(Normal(), N)
    z₂ ~ filldist(Normal(), N)
    z = [z₁ z₂]'
    σ_d ~ Exponential()
    ρ_d ~ LKJ(2, 8)
    L_ρ_d = cholesky(Symmetric(ρ_d)).L
    d = (σ_d .* L_ρ_d) * z

    λ_AB = exp.(a .+ gr[1, hidA] .+ gr[2, hidB] .+ d[1, did])
    λ_BA = exp.(a .+ gr[1, hidB] .+ gr[2, hidA] .+ d[2, did])
    for i ∈ eachindex(giftsAB)
        giftsAB[i] ~ Poisson(λ_AB[i])
        giftsBA[i] ~ Poisson(λ_BA[i])
    end
    return d
end

# ╔═╡ ee84ac32-58f1-49bc-b705-fbc709e0f11a
begin
	model = m14_7(
	    kl_data.N, kl_data.N_households, kl_data.hidA, kl_data.hidB, 
	    kl_data.did, kl_data.giftsAB, kl_data.giftsBA
	)
	m14_7_ch = sample(model, 
	    NUTS(1000, 0.65, init_ϵ=0.025), 
	    1000)
	m14_7_df = DataFrame(m14_7_ch);
end

# ╔═╡ 8448e4cd-0bce-4426-85db-72a40a279b1d
md" #### Code 14.32"

# ╔═╡ 640ac000-dd55-4dda-846f-303404360ab5
PRECIS(m14_7_df[:, r"_gr\[(1,2|2,1|1|2)\]"])

# ╔═╡ 038bc011-279e-492a-bbfc-074630cdff3e
md" #### Code 14.33"

# ╔═╡ c8d7399e-ad0d-4835-8fa0-1c8ad66e7d34
let
	g = [
	    m14_7_df.a .+ m14_7_df[!,"gr[1,$i]"]
	    for i ∈ 1:25
	]
	r = [
	    m14_7_df.a .+ m14_7_df[!,"gr[2,$i]"]
	    for i ∈ 1:25
	]
	g = hcat(g...)'
	r = hcat(r...)';
	Eg_μ = mean(eachcol(exp.(g)))
	Er_μ = mean(eachcol(exp.(r)));
	
	# Code 14.34
	
	# +
	plot(xlim=(0, 8.6), ylim=(0,8.6), xlab="generalized giving", ylab="generalized receiving")
	plot!(x -> x, c=:black, s=:dash)
	
	for i ∈ 1:25
	    gi = exp.(g[i,:])
	    ri = exp.(r[i,:])
	    Σ = cov([gi ri])
	    μ = [mean(gi), mean(ri)]
	
	    dt = acos(Σ[1,2])
	    xₜ(t) = Σ[1,1]*cos(t + dt/2) + μ[1]
	    yₜ(t) = Σ[2,2]*cos(t - dt/2) + μ[2]
	
	    plot!(xₜ, yₜ, 0, 2π, c=:black, lw=1)
	end
	
	scatter!(Eg_μ, Er_μ, c=:white, msw=1.5)
end

# ╔═╡ 1512c0e0-bee0-4fce-9062-39c60e43f3f8
md" #### Code 14.35"

# ╔═╡ 93a5e590-0ab0-4a13-8944-226258424f7d
PRECIS(m14_7_df[:, r"_d"])

# ╔═╡ aba1a47c-534b-4ce0-b41f-d68c3331207d
md" #### Code 14.36"

# ╔═╡ 2ff1b0f7-4a07-467f-bf0d-069c5b766ed1
#
# Illustrates `generated_quantities` trick to extract values returned from the model

let
	ch = Turing.MCMCChains.get_sections(m14_7_ch, :parameters)
	d_vals = generated_quantities(model, ch)
	
	d_y1 = [r[1,:] for r in d_vals]
	d_y1 = hcat(d_y1...)
	d_y1 = mean.(eachrow(d_y1))
	
	d_y2 = [r[2,:] for r in d_vals]
	d_y2 = hcat(d_y2...)
	d_y2 = mean.(eachrow(d_y2))
	
	scatter(d_y1, d_y2)
end

# ╔═╡ 0f77c94d-011e-4a55-99a1-0ee67acf63fb
md" ## 14.5 Continuous categories and the Gaussian process."

# ╔═╡ 00000000-0000-0000-0000-000000000001
PLUTO_PROJECT_TOML_CONTENTS = """
[deps]
CSV = "336ed68f-0bac-5ca0-87d4-7b16caf5d00b"
Dagitty = "d56128e0-8113-48cd-82a0-fc808dc30d4b"
DataFrames = "a93c6f00-e57d-5684-b7b6-d8193f3e46c0"
Distributions = "31c24e10-a181-5473-b8eb-7969acd0382f"
DrWatson = "634d3b9d-ee7a-5ddf-bec9-22491ea816e1"
LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
Logging = "56ddb016-857b-54e1-b83d-db4d58db5568"
Pkg = "44cfe95a-1eb2-52ea-b672-e2afdf69b78f"
Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
StatisticalRethinking = "2d09df54-9d0f-5258-8220-54c2a3d4fbee"
StatisticalRethinkingPlots = "e1a513d0-d9d9-49ff-a6dd-9d2e9db473da"
StatsBase = "2913bbd2-ae8a-5f71-8c99-4fb6c76f3a91"
StatsPlots = "f3b207a7-027a-5e70-b257-86293d7955fd"
Turing = "fce5fe82-541a-59a6-adf8-730c64b5f9a0"

[compat]
CSV = "~0.10.4"
Dagitty = "~0.0.1"
DataFrames = "~1.3.4"
Distributions = "~0.25.58"
DrWatson = "~2.9.1"
StatisticalRethinking = "~4.5.2"
StatisticalRethinkingPlots = "~1.0.1"
StatsBase = "~0.33.16"
StatsPlots = "~0.14.34"
Turing = "~0.21.1"
"""

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

julia_version = "1.9.0-DEV"
manifest_format = "2.0"
project_hash = "dd2bea27f6174ed1ba3b20ea7dad47db794fd951"

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

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

[[deps.AbstractMCMC]]
deps = ["BangBang", "ConsoleProgressMonitor", "Distributed", "Logging", "LoggingExtras", "ProgressLogging", "Random", "StatsBase", "TerminalLoggers", "Transducers"]
git-tree-sha1 = "47aca4cf0dc430f20f68f6992dc4af0e4dc8ebee"
uuid = "80f14c24-f653-4e6a-9b94-39d6b0f70001"
version = "4.0.0"

[[deps.AbstractPPL]]
deps = ["AbstractMCMC", "DensityInterface", "Setfield", "SparseArrays"]
git-tree-sha1 = "6320752437e9fbf49639a410017d862ad64415a5"
uuid = "7a57a42e-76ec-4ea3-a279-07e840d6d9cf"
version = "0.5.2"

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

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

[[deps.AdvancedHMC]]
deps = ["AbstractMCMC", "ArgCheck", "DocStringExtensions", "InplaceOps", "LinearAlgebra", "ProgressMeter", "Random", "Requires", "Setfield", "Statistics", "StatsBase", "StatsFuns", "UnPack"]
git-tree-sha1 = "345effa84030f273ee86fcdd706d8484ce9a1a3c"
uuid = "0bf59076-c3b1-5ca4-86bd-e02cd72cde3d"
version = "0.3.5"

[[deps.AdvancedMH]]
deps = ["AbstractMCMC", "Distributions", "Random", "Requires"]
git-tree-sha1 = "5d9e09a242d4cf222080398468244389c3428ed1"
uuid = "5b7e9947-ddc0-4b3f-9b55-0d8042f74170"
version = "0.6.7"

[[deps.AdvancedPS]]
deps = ["AbstractMCMC", "Distributions", "Libtask", "Random", "StatsFuns"]
git-tree-sha1 = "9ff1247be1e2aa2e740e84e8c18652bd9d55df22"
uuid = "576499cb-2369-40b2-a588-c64705576edc"
version = "0.3.8"

[[deps.AdvancedVI]]
deps = ["Bijectors", "Distributions", "DistributionsAD", "DocStringExtensions", "ForwardDiff", "LinearAlgebra", "ProgressMeter", "Random", "Requires", "StatsBase", "StatsFuns", "Tracker"]
git-tree-sha1 = "2f0ddff49ae4c812ba7b348b8427636f8bbd6c05"
uuid = "b5ca4192-6429-45e5-a2d9-87aec30a685c"
version = "0.1.4"

[[deps.ArgCheck]]
git-tree-sha1 = "a3a402a35a2f7e0b87828ccabbd5ebfbebe356b4"
uuid = "dce04be8-c92d-5529-be00-80e4d2c0e197"
version = "2.3.0"

[[deps.ArgTools]]
uuid = "0dad84c5-d112-42e6-8d28-ef12dabb789f"
version = "1.1.1"

[[deps.ArnoldiMethod]]
deps = ["LinearAlgebra", "Random", "StaticArrays"]
git-tree-sha1 = "f87e559f87a45bece9c9ed97458d3afe98b1ebb9"
uuid = "ec485272-7323-5ecc-a04f-4719b315124d"
version = "0.1.0"

[[deps.Arpack]]
deps = ["Arpack_jll", "Libdl", "LinearAlgebra", "Logging"]
git-tree-sha1 = "91ca22c4b8437da89b030f08d71db55a379ce958"
uuid = "7d9fca2a-8960-54d3-9f78-7d1dccf2cb97"
version = "0.5.3"

[[deps.Arpack_jll]]
deps = ["Artifacts", "CompilerSupportLibraries_jll", "JLLWrappers", "Libdl", "OpenBLAS_jll", "Pkg"]
git-tree-sha1 = "5ba6c757e8feccf03a1554dfaf3e26b3cfc7fd5e"
uuid = "68821587-b530-5797-8361-c406ea357684"
version = "3.5.1+1"

[[deps.ArrayInterface]]
deps = ["Compat", "IfElse", "LinearAlgebra", "Requires", "SparseArrays", "Static"]
git-tree-sha1 = "81f0cb60dc994ca17f68d9fb7c942a5ae70d9ee4"
uuid = "4fba245c-0d91-5ea0-9b3e-6abc04ee57a9"
version = "5.0.8"

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

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

[[deps.AxisArrays]]
deps = ["Dates", "IntervalSets", "IterTools", "RangeArrays"]
git-tree-sha1 = "cf6875678085aed97f52bfc493baaebeb6d40bcb"
uuid = "39de3d68-74b9-583c-8d2d-e117c070f3a9"
version = "0.4.5"

[[deps.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"

[[deps.BangBang]]
deps = ["Compat", "ConstructionBase", "Future", "InitialValues", "LinearAlgebra", "Requires", "Setfield", "Tables", "ZygoteRules"]
git-tree-sha1 = "b15a6bc52594f5e4a3b825858d1089618871bf9d"
uuid = "198e06fe-97b7-11e9-32a5-e1d131e6ad66"
version = "0.3.36"

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

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

[[deps.BenchmarkTools]]
deps = ["JSON", "Logging", "Printf", "Profile", "Statistics", "UUIDs"]
git-tree-sha1 = "4c10eee4af024676200bc7752e536f858c6b8f93"
uuid = "6e4b80f9-dd63-53aa-95a3-0cdb28fa8baf"
version = "1.3.1"

[[deps.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"

[[deps.BitTwiddlingConvenienceFunctions]]
deps = ["Static"]
git-tree-sha1 = "28bbdbf0354959db89358d1d79d421ff31ef0b5e"
uuid = "62783981-4cbd-42fc-bca8-16325de8dc4b"
version = "0.1.3"

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

[[deps.CPUSummary]]
deps = ["CpuId", "IfElse", "Static"]
git-tree-sha1 = "baaac45b4462b3b0be16726f38b789bf330fcb7a"
uuid = "2a0fbf3d-bb9c-48f3-b0a9-814d99fd7ab9"
version = "0.1.21"

[[deps.CSV]]
deps = ["CodecZlib", "Dates", "FilePathsBase", "InlineStrings", "Mmap", "Parsers", "PooledArrays", "SentinelArrays", "Tables", "Unicode", "WeakRefStrings"]
git-tree-sha1 = "873fb188a4b9d76549b81465b1f75c82aaf59238"
uuid = "336ed68f-0bac-5ca0-87d4-7b16caf5d00b"
version = "0.10.4"

[[deps.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"

[[deps.ChainRules]]
deps = ["ChainRulesCore", "Compat", "IrrationalConstants", "LinearAlgebra", "Random", "RealDot", "SparseArrays", "Statistics"]
git-tree-sha1 = "f4327ae7d92264a97665637002de789040106d87"
uuid = "082447d4-558c-5d27-93f4-14fc19e9eca2"
version = "1.29.0"

[[deps.ChainRulesCore]]
deps = ["Compat", "LinearAlgebra", "SparseArrays"]
git-tree-sha1 = "9950387274246d08af38f6eef8cb5480862a435f"
uuid = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
version = "1.14.0"

[[deps.ChangesOfVariables]]
deps = ["ChainRulesCore", "LinearAlgebra", "Test"]
git-tree-sha1 = "1e315e3f4b0b7ce40feded39c73049692126cf53"
uuid = "9e997f8a-9a97-42d5-a9f1-ce6bfc15e2c0"
version = "0.1.3"

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

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

[[deps.ColorSchemes]]
deps = ["ColorTypes", "ColorVectorSpace", "Colors", "FixedPointNumbers", "Random"]
git-tree-sha1 = "7297381ccb5df764549818d9a7d57e45f1057d30"
uuid = "35d6a980-a343-548e-a6ea-1d62b119f2f4"
version = "3.18.0"

[[deps.ColorTypes]]
deps = ["FixedPointNumbers", "Random"]
git-tree-sha1 = "32a2b8af383f11cbb65803883837a149d10dfe8a"
uuid = "3da002f7-5984-5a60-b8a6-cbb66c0b333f"
version = "0.10.12"

[[deps.ColorVectorSpace]]
deps = ["ColorTypes", "FixedPointNumbers", "LinearAlgebra", "SpecialFunctions", "Statistics", "TensorCore"]
git-tree-sha1 = "3f1f500312161f1ae067abe07d13b40f78f32e07"
uuid = "c3611d14-8923-5661-9e6a-0046d554d3a4"
version = "0.9.8"

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

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

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

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

[[deps.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 = "b153278a25dd42c65abbf4e62344f9d22e59191b"
uuid = "34da2185-b29b-5c13-b0c7-acf172513d20"
version = "3.43.0"

[[deps.CompatHelperLocal]]
deps = ["DocStringExtensions", "Pkg", "UUIDs"]
git-tree-sha1 = "908a50c2805d2571379fe1595585148c8352f63e"
uuid = "5224ae11-6099-4aaa-941d-3aab004bd678"
version = "0.1.20"

[[deps.CompilerSupportLibraries_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "e66e0078-7015-5450-92f7-15fbd957f2ae"
version = "0.5.2+0"

[[deps.Compose]]
deps = ["Base64", "Colors", "DataStructures", "Dates", "IterTools", "JSON", "LinearAlgebra", "Measures", "Printf", "Random", "Requires", "Statistics", "UUIDs"]
git-tree-sha1 = "9a2695195199f4f20b94898c8a8ac72609e165a4"
uuid = "a81c6b42-2e10-5240-aca2-a61377ecd94b"
version = "0.9.3"

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

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

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

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

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

[[deps.CpuId]]
deps = ["Markdown"]
git-tree-sha1 = "fcbb72b032692610bfbdb15018ac16a36cf2e406"
uuid = "adafc99b-e345-5852-983c-f28acb93d879"
version = "0.3.1"

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

[[deps.Dagitty]]
deps = ["BenchmarkTools", "Combinatorics", "Compose", "DataStructures", "Documenter", "GraphPlot", "LightGraphs", "Test"]
git-tree-sha1 = "c9746c7593c784cdd5502f2fb5a0dfdbfeb8eebf"
uuid = "d56128e0-8113-48cd-82a0-fc808dc30d4b"
version = "0.0.1"

[[deps.DataAPI]]
git-tree-sha1 = "fb5f5316dd3fd4c5e7c30a24d50643b73e37cd40"
uuid = "9a962f9c-6df0-11e9-0e5d-c546b8b5ee8a"
version = "1.10.0"

[[deps.DataFrames]]
deps = ["Compat", "DataAPI", "Future", "InvertedIndices", "IteratorInterfaceExtensions", "LinearAlgebra", "Markdown", "Missings", "PooledArrays", "PrettyTables", "Printf", "REPL", "Reexport", "SortingAlgorithms", "Statistics", "TableTraits", "Tables", "Unicode"]
git-tree-sha1 = "daa21eb85147f72e41f6352a57fccea377e310a9"
uuid = "a93c6f00-e57d-5684-b7b6-d8193f3e46c0"
version = "1.3.4"

[[deps.DataStructures]]
deps = ["Compat", "InteractiveUtils", "OrderedCollections"]
git-tree-sha1 = "cc1a8e22627f33c789ab60b36a9132ac050bbf75"
uuid = "864edb3b-99cc-5e75-8d2d-829cb0a9cfe8"
version = "0.18.12"

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

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

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

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

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

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

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

[[deps.DiffRules]]
deps = ["IrrationalConstants", "LogExpFunctions", "NaNMath", "Random", "SpecialFunctions"]
git-tree-sha1 = "28d605d9a0ac17118fe2c5e9ce0fbb76c3ceb120"
uuid = "b552c78f-8df3-52c6-915a-8e097449b14b"
version = "1.11.0"

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

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

[[deps.Distributions]]
deps = ["ChainRulesCore", "DensityInterface", "FillArrays", "LinearAlgebra", "PDMats", "Printf", "QuadGK", "Random", "SparseArrays", "SpecialFunctions", "Statistics", "StatsBase", "StatsFuns", "Test"]
git-tree-sha1 = "8a6b49396a4058771c5c072239b2e0a76e2e898c"
uuid = "31c24e10-a181-5473-b8eb-7969acd0382f"
version = "0.25.58"

[[deps.DistributionsAD]]
deps = ["Adapt", "ChainRules", "ChainRulesCore", "Compat", "DiffRules", "Distributions", "FillArrays", "LinearAlgebra", "NaNMath", "PDMats", "Random", "Requires", "SpecialFunctions", "StaticArrays", "StatsBase", "StatsFuns", "ZygoteRules"]
git-tree-sha1 = "a20d1374e896c72d2598feaf8e86b6d58a0c7d0a"
uuid = "ced4e74d-a319-5a8a-b0ac-84af2272839c"
version = "0.6.39"

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

[[deps.Documenter]]
deps = ["ANSIColoredPrinters", "Base64", "Dates", "DocStringExtensions", "IOCapture", "InteractiveUtils", "JSON", "LibGit2", "Logging", "Markdown", "REPL", "Test", "Unicode"]
git-tree-sha1 = "122d031e8dcb2d3e767ed434bc4d1ae1788b5a7f"
uuid = "e30172f5-a6a5-5a46-863b-614d45cd2de4"
version = "0.27.17"

[[deps.Downloads]]
deps = ["ArgTools", "FileWatching", "LibCURL", "NetworkOptions"]
uuid = "f43a241f-c20a-4ad4-852c-f6b1247861c6"
version = "1.6.0"

[[deps.DrWatson]]
deps = ["Dates", "FileIO", "JLD2", "LibGit2", "MacroTools", "Pkg", "Random", "Requires", "Scratch", "UnPack"]
git-tree-sha1 = "67e9001646db6e45006643bf37716ecd831d37d2"
uuid = "634d3b9d-ee7a-5ddf-bec9-22491ea816e1"
version = "2.9.1"

[[deps.DynamicPPL]]
deps = ["AbstractMCMC", "AbstractPPL", "BangBang", "Bijectors", "ChainRulesCore", "Distributions", "LinearAlgebra", "MacroTools", "Random", "Setfield", "Test", "ZygoteRules"]
git-tree-sha1 = "5d1704965e4bf0c910693b09ece8163d75e28806"
uuid = "366bfd00-2699-11ea-058f-f148b4cae6d8"
version = "0.19.1"

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

[[deps.EllipsisNotation]]
deps = ["ArrayInterface"]
git-tree-sha1 = "d064b0340db45d48893e7604ec95e7a2dc9da904"
uuid = "da5c29d0-fa7d-589e-88eb-ea29b0a81949"
version = "1.5.0"

[[deps.EllipticalSliceSampling]]
deps = ["AbstractMCMC", "ArrayInterface", "Distributions", "Random", "Statistics"]
git-tree-sha1 = "bed775e32c6f38a19c1dbe0298480798e6be455f"
uuid = "cad2338a-1db2-11e9-3401-43bc07c9ede2"
version = "0.5.0"

[[deps.Expat_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "bad72f730e9e91c08d9427d5e8db95478a3c323d"
uuid = "2e619515-83b5-522b-bb60-26c02a35a201"
version = "2.4.8+0"

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

[[deps.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"

[[deps.FFTW]]
deps = ["AbstractFFTs", "FFTW_jll", "LinearAlgebra", "MKL_jll", "Preferences", "Reexport"]
git-tree-sha1 = "505876577b5481e50d089c1c68899dfb6faebc62"
uuid = "7a1cc6ca-52ef-59f5-83cd-3a7055c09341"
version = "1.4.6"

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

[[deps.FileIO]]
deps = ["Pkg", "Requires", "UUIDs"]
git-tree-sha1 = "9267e5f50b0e12fdfd5a2455534345c4cf2c7f7a"
uuid = "5789e2e9-d7fb-5bc7-8068-2c6fae9b9549"
version = "1.14.0"

[[deps.FilePathsBase]]
deps = ["Compat", "Dates", "Mmap", "Printf", "Test", "UUIDs"]
git-tree-sha1 = "129b104185df66e408edd6625d480b7f9e9823a0"
uuid = "48062228-2e41-5def-b9a4-89aafe57970f"
version = "0.9.18"

[[deps.FileWatching]]
uuid = "7b1f6079-737a-58dc-b8bc-7a2ca5c1b5ee"

[[deps.FillArrays]]
deps = ["LinearAlgebra", "Random", "SparseArrays", "Statistics"]
git-tree-sha1 = "246621d23d1f43e3b9c368bf3b72b2331a27c286"
uuid = "1a297f60-69ca-5386-bcde-b61e274b549b"
version = "0.13.2"

[[deps.FiniteDiff]]
deps = ["ArrayInterface", "LinearAlgebra", "Requires", "SparseArrays", "StaticArrays"]
git-tree-sha1 = "51c8f36c81badaa0e9ec405dcbabaf345ed18c84"
uuid = "6a86dc24-6348-571c-b903-95158fe2bd41"
version = "2.11.1"

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

[[deps.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"

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

[[deps.ForwardDiff]]
deps = ["CommonSubexpressions", "DiffResults", "DiffRules", "LinearAlgebra", "LogExpFunctions", "NaNMath", "Preferences", "Printf", "Random", "SpecialFunctions", "StaticArrays"]
git-tree-sha1 = "7a380de46b0a1db85c59ebbce5788412a39e4cb7"
uuid = "f6369f11-7733-5829-9624-2563aa707210"
version = "0.10.28"

[[deps.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"

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

[[deps.Functors]]
git-tree-sha1 = "223fffa49ca0ff9ce4f875be001ffe173b2b7de4"
uuid = "d9f16b24-f501-4c13-a1f2-28368ffc5196"
version = "0.2.8"

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

[[deps.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"

[[deps.GR]]
deps = ["Base64", "DelimitedFiles", "GR_jll", "HTTP", "JSON", "Libdl", "LinearAlgebra", "Pkg", "Printf", "Random", "RelocatableFolders", "Serialization", "Sockets", "Test", "UUIDs"]
git-tree-sha1 = "af237c08bda486b74318c8070adb96efa6952530"
uuid = "28b8d3ca-fb5f-59d9-8090-bfdbd6d07a71"
version = "0.64.2"

[[deps.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 = "cd6efcf9dc746b06709df14e462f0a3fe0786b1e"
uuid = "d2c73de3-f751-5644-a686-071e5b155ba9"
version = "0.64.2+0"

[[deps.GeometryBasics]]
deps = ["EarCut_jll", "IterTools", "LinearAlgebra", "StaticArrays", "StructArrays", "Tables"]
git-tree-sha1 = "83ea630384a13fc4f002b77690bc0afeb4255ac9"
uuid = "5c1252a2-5f33-56bf-86c9-59e7332b4326"
version = "0.4.2"

[[deps.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"

[[deps.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"

[[deps.GraphPlot]]
deps = ["ArnoldiMethod", "ColorTypes", "Colors", "Compose", "DelimitedFiles", "LightGraphs", "LinearAlgebra", "Random", "SparseArrays"]
git-tree-sha1 = "dd8f15128a91b0079dfe3f4a4a1e190e54ac7164"
uuid = "a2cc645c-3eea-5389-862e-a155d0052231"
version = "0.4.4"

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

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

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

[[deps.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"

[[deps.HostCPUFeatures]]
deps = ["BitTwiddlingConvenienceFunctions", "IfElse", "Libdl", "Static"]
git-tree-sha1 = "18be5268cf415b5e27f34980ed25a7d34261aa83"
uuid = "3e5b6fbb-0976-4d2c-9146-d79de83f2fb0"
version = "0.1.7"

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

[[deps.Hwloc_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "303d70c961317c4c20fafaf5dbe0e6d610c38542"
uuid = "e33a78d0-f292-5ffc-b300-72abe9b543c8"
version = "2.7.1+0"

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

[[deps.IRTools]]
deps = ["InteractiveUtils", "MacroTools", "Test"]
git-tree-sha1 = "af14a478780ca78d5eb9908b263023096c2b9d64"
uuid = "7869d1d1-7146-5819-86e3-90919afe41df"
version = "0.4.6"

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

[[deps.Inflate]]
git-tree-sha1 = "f5fc07d4e706b84f72d54eedcc1c13d92fb0871c"
uuid = "d25df0c9-e2be-5dd7-82c8-3ad0b3e990b9"
version = "0.1.2"

[[deps.IniFile]]
git-tree-sha1 = "f550e6e32074c939295eb5ea6de31849ac2c9625"
uuid = "83e8ac13-25f8-5344-8a64-a9f2b223428f"
version = "0.5.1"

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

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

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

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

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

[[deps.Interpolations]]
deps = ["AxisAlgorithms", "ChainRulesCore", "LinearAlgebra", "OffsetArrays", "Random", "Ratios", "Requires", "SharedArrays", "SparseArrays", "StaticArrays", "WoodburyMatrices"]
git-tree-sha1 = "b7bc05649af456efc75d178846f47006c2c4c3c7"
uuid = "a98d9a8b-a2ab-59e6-89dd-64a1c18fca59"
version = "0.13.6"

[[deps.IntervalSets]]
deps = ["Dates", "EllipsisNotation", "Statistics"]
git-tree-sha1 = "bcf640979ee55b652f3b01650444eb7bbe3ea837"
uuid = "8197267c-284f-5f27-9208-e0e47529a953"
version = "0.5.4"

[[deps.InverseFunctions]]
deps = ["Test"]
git-tree-sha1 = "336cc738f03e069ef2cac55a104eb823455dca75"
uuid = "3587e190-3f89-42d0-90ee-14403ec27112"
version = "0.1.4"

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

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

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

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

[[deps.JLD2]]
deps = ["FileIO", "MacroTools", "Mmap", "OrderedCollections", "Pkg", "Printf", "Reexport", "TranscodingStreams", "UUIDs"]
git-tree-sha1 = "81b9477b49402b47fbe7f7ae0b252077f53e4a08"
uuid = "033835bb-8acc-5ee8-8aae-3f567f8a3819"
version = "0.4.22"

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

[[deps.JSON]]
deps = ["Dates", "Mmap", "Parsers", "Unicode"]
git-tree-sha1 = "3c837543ddb02250ef42f4738347454f95079d4e"
uuid = "682c06a0-de6a-54ab-a142-c8b1cf79cde6"
version = "0.21.3"

[[deps.JpegTurbo_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "b53380851c6e6664204efb2e62cd24fa5c47e4ba"
uuid = "aacddb02-875f-59d6-b918-886e6ef4fbf8"
version = "2.1.2+0"

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

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

[[deps.LERC_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "bf36f528eec6634efc60d7ec062008f171071434"
uuid = "88015f11-f218-50d7-93a8-a6af411a945d"
version = "3.0.0+1"

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

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

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

[[deps.Latexify]]
deps = ["Formatting", "InteractiveUtils", "LaTeXStrings", "MacroTools", "Markdown", "Printf", "Requires"]
git-tree-sha1 = "46a39b9c58749eefb5f2dc1178cb8fab5332b1ab"
uuid = "23fbe1c1-3f47-55db-b15f-69d7ec21a316"
version = "0.15.15"

[[deps.LayoutPointers]]
deps = ["ArrayInterface", "LinearAlgebra", "ManualMemory", "SIMDTypes", "Static"]
git-tree-sha1 = "b651f573812d6c36c22c944dd66ef3ab2283dfa1"
uuid = "10f19ff3-798f-405d-979b-55457f8fc047"
version = "0.1.6"

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

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

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

[[deps.LibCURL]]
deps = ["LibCURL_jll", "MozillaCACerts_jll"]
uuid = "b27032c2-a3e7-50c8-80cd-2d36dbcbfd21"
version = "0.6.3"

[[deps.LibCURL_jll]]
deps = ["Artifacts", "LibSSH2_jll", "Libdl", "MbedTLS_jll", "Zlib_jll", "nghttp2_jll"]
uuid = "deac9b47-8bc7-5906-a0fe-35ac56dc84c0"
version = "7.81.0+0"

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

[[deps.LibSSH2_jll]]
deps = ["Artifacts", "Libdl", "MbedTLS_jll"]
uuid = "29816b5a-b9ab-546f-933c-edad1886dfa8"
version = "1.10.2+0"

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

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

[[deps.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"

[[deps.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"

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

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

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

[[deps.Libtask]]
deps = ["IRTools", "LRUCache", "LinearAlgebra", "MacroTools", "Statistics"]
git-tree-sha1 = "ed1b54f6df6fb7af8b315cfdc288ab5572dbd3ba"
uuid = "6f1fad26-d15e-5dc8-ae53-837a1d7b8c9f"
version = "0.7.0"

[[deps.Libtiff_jll]]
deps = ["Artifacts", "JLLWrappers", "JpegTurbo_jll", "LERC_jll", "Libdl", "Pkg", "Zlib_jll", "Zstd_jll"]
git-tree-sha1 = "c9551dd26e31ab17b86cbd00c2ede019c08758eb"
uuid = "89763e89-9b03-5906-acba-b20f662cd828"
version = "4.3.0+1"

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

[[deps.LightGraphs]]
deps = ["ArnoldiMethod", "DataStructures", "Distributed", "Inflate", "LinearAlgebra", "Random", "SharedArrays", "SimpleTraits", "SparseArrays", "Statistics"]
git-tree-sha1 = "432428df5f360964040ed60418dd5601ecd240b6"
uuid = "093fc24a-ae57-5d10-9952-331d41423f4d"
version = "1.3.5"

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

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

[[deps.LogExpFunctions]]
deps = ["ChainRulesCore", "ChangesOfVariables", "DocStringExtensions", "InverseFunctions", "IrrationalConstants", "LinearAlgebra"]
git-tree-sha1 = "76c987446e8d555677f064aaac1145c4c17662f8"
uuid = "2ab3a3ac-af41-5b50-aa03-7779005ae688"
version = "0.3.14"

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

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

[[deps.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 = "a9e3f4a3460b08dc75870811635b83afbd388ee8"
uuid = "c7f686f2-ff18-58e9-bc7b-31028e88f75d"
version = "5.3.0"

[[deps.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"

[[deps.MKL_jll]]
deps = ["Artifacts", "IntelOpenMP_jll", "JLLWrappers", "LazyArtifacts", "Libdl", "Pkg"]
git-tree-sha1 = "e595b205efd49508358f7dc670a940c790204629"
uuid = "856f044c-d86e-5d09-b602-aeab76dc8ba7"
version = "2022.0.0+0"

[[deps.MLJModelInterface]]
deps = ["Random", "ScientificTypesBase", "StatisticalTraits"]
git-tree-sha1 = "74d7fb54c306af241c5f9d4816b735cb4051e125"
uuid = "e80e1ace-859a-464e-9ed9-23947d8ae3ea"
version = "1.4.2"

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

[[deps.ManualMemory]]
git-tree-sha1 = "bcaef4fc7a0cfe2cba636d84cda54b5e4e4ca3cd"
uuid = "d125e4d3-2237-4719-b19c-fa641b8a4667"
version = "0.1.8"

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

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

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

[[deps.MbedTLS_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "c8ffd9c3-330d-5841-b78e-0817d7145fa1"
version = "2.28.0+0"

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

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

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

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

[[deps.MonteCarloMeasurements]]
deps = ["Distributed", "Distributions", "LinearAlgebra", "MacroTools", "Random", "RecipesBase", "Requires", "SLEEFPirates", "StaticArrays", "Statistics", "StatsBase", "Test"]
git-tree-sha1 = "03619e255664666b352a5e5f6b45e8b00d439870"
uuid = "0987c9cc-fe09-11e8-30f0-b96dd679fdca"
version = "1.0.8"

[[deps.MozillaCACerts_jll]]
uuid = "14a3606d-f60d-562e-9121-12d972cd8159"
version = "2022.2.1"

[[deps.MultivariateStats]]
deps = ["Arpack", "LinearAlgebra", "SparseArrays", "Statistics", "StatsBase"]
git-tree-sha1 = "6d019f5a0465522bbfdd68ecfad7f86b535d6935"
uuid = "6f286f6a-111f-5878-ab1e-185364afe411"
version = "0.9.0"

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

[[deps.NNlib]]
deps = ["Adapt", "ChainRulesCore", "Compat", "LinearAlgebra", "Pkg", "Requires", "Statistics"]
git-tree-sha1 = "f89de462a7bc3243f95834e75751d70b3a33e59d"
uuid = "872c559c-99b0-510c-b3b7-b6c96a88d5cd"
version = "0.8.5"

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

[[deps.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"

[[deps.NamedDims]]
deps = ["AbstractFFTs", "ChainRulesCore", "CovarianceEstimation", "LinearAlgebra", "Pkg", "Requires", "Statistics"]
git-tree-sha1 = "0856b62716585eb90cc1dada226ac9eab5f69aa5"
uuid = "356022a1-0364-5f58-8944-0da4b18d706f"
version = "0.2.47"

[[deps.NamedTupleTools]]
git-tree-sha1 = "befc30261949849408ac945a1ebb9fa5ec5e1fd5"
uuid = "d9ec5142-1e00-5aa0-9d6a-321866360f50"
version = "0.14.0"

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

[[deps.NearestNeighbors]]
deps = ["Distances", "StaticArrays"]
git-tree-sha1 = "ded92de95031d4a8c61dfb6ba9adb6f1d8016ddd"
uuid = "b8a86587-4115-5ab1-83bc-aa920d37bbce"
version = "0.4.10"

[[deps.NetworkOptions]]
uuid = "ca575930-c2e3-43a9-ace4-1e988b2c1908"
version = "1.2.0"

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

[[deps.OffsetArrays]]
deps = ["Adapt"]
git-tree-sha1 = "aee446d0b3d5764e35289762f6a18e8ea041a592"
uuid = "6fe1bfb0-de20-5000-8ca7-80f57d26f881"
version = "1.11.0"

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

[[deps.OpenBLAS_jll]]
deps = ["Artifacts", "CompilerSupportLibraries_jll", "Libdl"]
uuid = "4536629a-c528-5b80-bd46-f80d51c5b363"
version = "0.3.20+0"

[[deps.OpenLibm_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "05823500-19ac-5b8b-9628-191a04bc5112"
version = "0.8.1+0"

[[deps.OpenSSL_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "ab05aa4cc89736e95915b01e7279e61b1bfe33b8"
uuid = "458c3c95-2e84-50aa-8efc-19380b2a3a95"
version = "1.1.14+0"

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

[[deps.Optim]]
deps = ["Compat", "FillArrays", "ForwardDiff", "LineSearches", "LinearAlgebra", "NLSolversBase", "NaNMath", "Parameters", "PositiveFactorizations", "Printf", "SparseArrays", "StatsBase"]
git-tree-sha1 = "7a28efc8e34d5df89fc87343318b0a8add2c4021"
uuid = "429524aa-4258-5aef-a3af-852621145aeb"
version = "1.7.0"

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

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

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

[[deps.PDMats]]
deps = ["LinearAlgebra", "SparseArrays", "SuiteSparse"]
git-tree-sha1 = "c8c62e4aa5bbd0e48bafe294d4325fc87194a5ed"
uuid = "90014a1f-27ba-587c-ab20-58faa44d9150"
version = "0.11.9"

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

[[deps.ParetoSmooth]]
deps = ["AxisKeys", "InteractiveUtils", "LinearAlgebra", "LogExpFunctions", "MCMCDiagnosticTools", "NamedDims", "PrettyTables", "Printf", "Random", "Requires", "Statistics", "StatsBase", "Tullio"]
git-tree-sha1 = "832b20efeb8bc495cada4b412383cb4454c2897c"
uuid = "a68b5a21-f429-434e-8bfa-46b447300aac"
version = "0.7.1"

[[deps.ParetoSmoothedImportanceSampling]]
deps = ["CSV", "DataFrames", "Distributions", "JSON", "Printf", "Random", "StanSample", "Statistics", "StatsFuns", "StatsPlots", "Test"]
git-tree-sha1 = "48d5459d3d759a37f501bc906928d3abb59b1714"
uuid = "98f080ec-61e2-11eb-1c7b-31ea1097256f"
version = "1.3.2"

[[deps.Parsers]]
deps = ["Dates"]
git-tree-sha1 = "1285416549ccfcdf0c50d4997a94331e88d68413"
uuid = "69de0a69-1ddd-5017-9359-2bf0b02dc9f0"
version = "2.3.1"

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

[[deps.Pkg]]
deps = ["Artifacts", "Dates", "Downloads", "FileWatching", "LibGit2", "Libdl", "Logging", "Markdown", "Printf", "REPL", "Random", "SHA", "Serialization", "TOML", "Tar", "UUIDs", "p7zip_jll"]
uuid = "44cfe95a-1eb2-52ea-b672-e2afdf69b78f"
version = "1.8.0"

[[deps.PlotThemes]]
deps = ["PlotUtils", "Statistics"]
git-tree-sha1 = "8162b2f8547bc23876edd0c5181b27702ae58dce"
uuid = "ccf2f8ad-2431-5c83-bf29-c5338b663b6a"
version = "3.0.0"

[[deps.PlotUtils]]
deps = ["ColorSchemes", "Colors", "Dates", "Printf", "Random", "Reexport", "Statistics"]
git-tree-sha1 = "bb16469fd5224100e422f0b027d26c5a25de1200"
uuid = "995b91a9-d308-5afd-9ec6-746e21dbc043"
version = "1.2.0"

[[deps.Plots]]
deps = ["Base64", "Contour", "Dates", "Downloads", "FFMPEG", "FixedPointNumbers", "GR", "GeometryBasics", "JSON", "Latexify", "LinearAlgebra", "Measures", "NaNMath", "Pkg", "PlotThemes", "PlotUtils", "Printf", "REPL", "Random", "RecipesBase", "RecipesPipeline", "Reexport", "Requires", "Scratch", "Showoff", "SparseArrays", "Statistics", "StatsBase", "UUIDs", "UnicodeFun", "Unzip"]
git-tree-sha1 = "d457f881ea56bbfa18222642de51e0abf67b9027"
uuid = "91a5bcdd-55d7-5caf-9e0b-520d859cae80"
version = "1.29.0"

[[deps.PooledArrays]]
deps = ["DataAPI", "Future"]
git-tree-sha1 = "a6062fe4063cdafe78f4a0a81cfffb89721b30e7"
uuid = "2dfb63ee-cc39-5dd5-95bd-886bf059d720"
version = "1.4.2"

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

[[deps.Preferences]]
deps = ["TOML"]
git-tree-sha1 = "47e5f437cc0e7ef2ce8406ce1e7e24d44915f88d"
uuid = "21216c6a-2e73-6563-6e65-726566657250"
version = "1.3.0"

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

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

[[deps.Profile]]
deps = ["Printf"]
uuid = "9abbd945-dff8-562f-b5e8-e1ebf5ef1b79"

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

[[deps.ProgressMeter]]
deps = ["Distributed", "Printf"]
git-tree-sha1 = "d7a7aef8f8f2d537104f170139553b14dfe39fe9"
uuid = "92933f4c-e287-5a05-a399-4b506db050ca"
version = "1.7.2"

[[deps.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 = "c6c0f690d0cc7caddb74cef7aa847b824a16b256"
uuid = "ea2cea3b-5b76-57ae-a6ef-0a8af62496e1"
version = "5.15.3+1"

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

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

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

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

[[deps.Ratios]]
deps = ["Requires"]
git-tree-sha1 = "dc84268fe0e3335a62e315a3a7cf2afa7178a734"
uuid = "c84ed2f1-dad5-54f0-aa8e-dbefe2724439"
version = "0.4.3"

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

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

[[deps.RecipesPipeline]]
deps = ["Dates", "NaNMath", "PlotUtils", "RecipesBase"]
git-tree-sha1 = "dc1e451e15d90347a7decc4221842a022b011714"
uuid = "01d81517-befc-4cb6-b9ec-a95719d0359c"
version = "0.5.2"

[[deps.RecursiveArrayTools]]
deps = ["Adapt", "ArrayInterface", "ChainRulesCore", "DocStringExtensions", "FillArrays", "LinearAlgebra", "RecipesBase", "Requires", "StaticArrays", "Statistics", "ZygoteRules"]
git-tree-sha1 = "bfe14f127f3e7def02a6c2b1940b39d0dabaa3ef"
uuid = "731186ca-8d62-57ce-b412-fbd966d074cd"
version = "2.26.3"

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

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

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

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

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

[[deps.Roots]]
deps = ["CommonSolve", "Printf", "Setfield"]
git-tree-sha1 = "838b60ee62bebc794864c880a47e331e00c47505"
uuid = "f2b01f46-fcfa-551c-844a-d8ac1e96c665"
version = "1.4.1"

[[deps.SHA]]
uuid = "ea8e919c-243c-51af-8825-aaa63cd721ce"
version = "0.7.0"

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

[[deps.SLEEFPirates]]
deps = ["IfElse", "Static", "VectorizationBase"]
git-tree-sha1 = "ac399b5b163b9140f9c310dfe9e9aaa225617ff6"
uuid = "476501e8-09a2-5ece-8869-fb82de89a1fa"
version = "0.6.32"

[[deps.SciMLBase]]
deps = ["ArrayInterface", "CommonSolve", "ConstructionBase", "Distributed", "DocStringExtensions", "IteratorInterfaceExtensions", "LinearAlgebra", "Logging", "Markdown", "RecipesBase", "RecursiveArrayTools", "StaticArrays", "Statistics", "Tables", "TreeViews"]
git-tree-sha1 = "5420ffd1d5ad49e2c8309efb7338cc2443487029"
uuid = "0bca4576-84f4-4d90-8ffe-ffa030f20462"
version = "1.31.4"

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

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

[[deps.SentinelArrays]]
deps = ["Dates", "Random"]
git-tree-sha1 = "6a2f7d70512d205ca8c7ee31bfa9f142fe74310c"
uuid = "91c51154-3ec4-41a3-a24f-3f23e20d615c"
version = "1.3.12"

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

[[deps.Setfield]]
deps = ["ConstructionBase", "Future", "MacroTools", "Requires"]
git-tree-sha1 = "38d88503f695eb0301479bc9b0d4320b378bafe5"
uuid = "efcf1570-3423-57d1-acb7-fd33fddbac46"
version = "0.8.2"

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

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

[[deps.SimpleTraits]]
deps = ["InteractiveUtils", "MacroTools"]
git-tree-sha1 = "5d7e3f4e11935503d3ecaf7186eac40602e7d231"
uuid = "699a6c99-e7fa-54fc-8d76-47d257e15c1d"
version = "0.9.4"

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

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

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

[[deps.SpecialFunctions]]
deps = ["ChainRulesCore", "IrrationalConstants", "LogExpFunctions", "OpenLibm_jll", "OpenSpecFun_jll"]
git-tree-sha1 = "5ba658aeecaaf96923dce0da9e703bd1fe7666f9"
uuid = "276daf66-3868-5448-9aa4-cd146d93841b"
version = "2.1.4"

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

[[deps.StanBase]]
deps = ["CSV", "DataFrames", "DelimitedFiles", "Distributed", "DocStringExtensions", "Documenter", "JSON", "Parameters", "Random", "StanDump", "Unicode"]
git-tree-sha1 = "352c902eec97313f9d9024fe81089dc67199d01c"
uuid = "d0ee94f6-a23d-54aa-bbe9-7f572d6da7f5"
version = "4.5.0"

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

[[deps.StanSample]]
deps = ["CSV", "CompatHelperLocal", "DataFrames", "DelimitedFiles", "Distributed", "DocStringExtensions", "JSON", "MonteCarloMeasurements", "NamedTupleTools", "OrderedCollections", "Parameters", "Random", "Reexport", "Requires", "StanBase", "StanDump", "StatsFuns", "TableOperations", "Tables", "Unicode"]
git-tree-sha1 = "8ca5b9e48d2d629e3a77027f8749ad4889387e45"
uuid = "c1514b29-d3a0-5178-b312-660c88baa699"
version = "6.5.0"

[[deps.Static]]
deps = ["IfElse"]
git-tree-sha1 = "5309da1cdef03e95b73cd3251ac3a39f887da53e"
uuid = "aedffcd0-7271-4cad-89d0-dc628f76c6d3"
version = "0.6.4"

[[deps.StaticArrays]]
deps = ["LinearAlgebra", "Random", "Statistics"]
git-tree-sha1 = "cd56bf18ed715e8b09f06ef8c6b781e6cdc49911"
uuid = "90137ffa-7385-5640-81b9-e52037218182"
version = "1.4.4"

[[deps.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 = "ba0b8c8b19dc36a9207c668af32176af2a92da8e"
uuid = "2d09df54-9d0f-5258-8220-54c2a3d4fbee"
version = "4.5.2"

[[deps.StatisticalRethinkingPlots]]
deps = ["Distributions", "DocStringExtensions", "KernelDensity", "LaTeXStrings", "Parameters", "Plots", "Reexport", "Requires", "StatisticalRethinking", "StatsPlots"]
git-tree-sha1 = "4df7bd9b96a675715534ca051c1c3074db0de88c"
uuid = "e1a513d0-d9d9-49ff-a6dd-9d2e9db473da"
version = "1.0.1"

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

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

[[deps.StatsAPI]]
deps = ["LinearAlgebra"]
git-tree-sha1 = "c82aaa13b44ea00134f8c9c89819477bd3986ecd"
uuid = "82ae8749-77ed-4fe6-ae5f-f523153014b0"
version = "1.3.0"

[[deps.StatsBase]]
deps = ["DataAPI", "DataStructures", "LinearAlgebra", "LogExpFunctions", "Missings", "Printf", "Random", "SortingAlgorithms", "SparseArrays", "Statistics", "StatsAPI"]
git-tree-sha1 = "8977b17906b0a1cc74ab2e3a05faa16cf08a8291"
uuid = "2913bbd2-ae8a-5f71-8c99-4fb6c76f3a91"
version = "0.33.16"

[[deps.StatsFuns]]
deps = ["ChainRulesCore", "InverseFunctions", "IrrationalConstants", "LogExpFunctions", "Reexport", "Rmath", "SpecialFunctions"]
git-tree-sha1 = "5950925ff997ed6fb3e985dcce8eb1ba42a0bbe7"
uuid = "4c63d2b9-4356-54db-8cca-17b64c39e42c"
version = "0.9.18"

[[deps.StatsPlots]]
deps = ["AbstractFFTs", "Clustering", "DataStructures", "DataValues", "Distributions", "Interpolations", "KernelDensity", "LinearAlgebra", "MultivariateStats", "Observables", "Plots", "RecipesBase", "RecipesPipeline", "Reexport", "StatsBase", "TableOperations", "Tables", "Widgets"]
git-tree-sha1 = "43a316e07ae612c461fd874740aeef396c60f5f8"
uuid = "f3b207a7-027a-5e70-b257-86293d7955fd"
version = "0.14.34"

[[deps.StructArrays]]
deps = ["Adapt", "DataAPI", "StaticArrays", "Tables"]
git-tree-sha1 = "e75d82493681dfd884a357952bbd7ab0608e1dc3"
uuid = "09ab397b-f2b6-538f-b94a-2f83cf4a842a"
version = "0.6.7"

[[deps.StructuralCausalModels]]
deps = ["CSV", "Combinatorics", "DataFrames", "DataStructures", "Distributions", "DocStringExtensions", "LinearAlgebra", "NamedArrays", "Reexport", "Statistics"]
git-tree-sha1 = "5ec7266296539dab3af599106886f74b57f9b1cf"
uuid = "a41e6734-49ce-4065-8b83-aff084c01dfd"
version = "1.3.1"

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

[[deps.TOML]]
deps = ["Dates"]
uuid = "fa267f1f-6049-4f14-aa54-33bafae1ed76"
version = "1.0.0"

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

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

[[deps.Tables]]
deps = ["DataAPI", "DataValueInterfaces", "IteratorInterfaceExtensions", "LinearAlgebra", "OrderedCollections", "TableTraits", "Test"]
git-tree-sha1 = "5ce79ce186cc678bbb5c5681ca3379d1ddae11a1"
uuid = "bd369af6-aec1-5ad0-b16a-f7cc5008161c"
version = "1.7.0"

[[deps.Tar]]
deps = ["ArgTools", "SHA"]
uuid = "a4e569a6-e804-4fa4-b0f3-eef7a1d5b13e"
version = "1.10.0"

[[deps.TensorCore]]
deps = ["LinearAlgebra"]
git-tree-sha1 = "1feb45f88d133a655e001435632f019a9a1bcdb6"
uuid = "62fd8b95-f654-4bbd-a8a5-9c27f68ccd50"
version = "0.1.1"

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

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

[[deps.Tracker]]
deps = ["Adapt", "DiffRules", "ForwardDiff", "LinearAlgebra", "LogExpFunctions", "MacroTools", "NNlib", "NaNMath", "Printf", "Random", "Requires", "SpecialFunctions", "Statistics"]
git-tree-sha1 = "0874c1b5de1b5529b776cfeca3ec0acfada97b1b"
uuid = "9f7883ad-71c0-57eb-9f7f-b5c9e6d3789c"
version = "0.2.20"

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

[[deps.Transducers]]
deps = ["Adapt", "ArgCheck", "BangBang", "Baselet", "CompositionsBase", "DefineSingletons", "Distributed", "InitialValues", "Logging", "Markdown", "MicroCollections", "Requires", "Setfield", "SplittablesBase", "Tables"]
git-tree-sha1 = "c76399a3bbe6f5a88faa33c8f8a65aa631d95013"
uuid = "28d57a85-8fef-5791-bfe6-a80928e7c999"
version = "0.4.73"

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

[[deps.Tullio]]
deps = ["ChainRulesCore", "DiffRules", "LinearAlgebra", "Requires"]
git-tree-sha1 = "859e2e9a7222553a0c052e423557cedb49376da9"
uuid = "bc48ee85-29a4-5162-ae0b-a64e1601d4bc"
version = "0.3.4"

[[deps.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 = "ef0fdc72023c4480a9372f32db88cce68b186e8a"
uuid = "fce5fe82-541a-59a6-adf8-730c64b5f9a0"
version = "0.21.1"

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

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

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

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

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

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

[[deps.VectorizationBase]]
deps = ["ArrayInterface", "CPUSummary", "HostCPUFeatures", "Hwloc", "IfElse", "LayoutPointers", "Libdl", "LinearAlgebra", "SIMDTypes", "Static"]
git-tree-sha1 = "ff34c2f1d80ccb4f359df43ed65d6f90cb70b323"
uuid = "3d5dd08c-fd9d-11e8-17fa-ed2836048c2f"
version = "0.21.31"

[[deps.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"

[[deps.Wayland_protocols_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "4528479aa01ee1b3b4cd0e6faef0e04cf16466da"
uuid = "2381bf8a-dfd0-557d-9999-79630e7b1b91"
version = "1.25.0+0"

[[deps.WeakRefStrings]]
deps = ["DataAPI", "InlineStrings", "Parsers"]
git-tree-sha1 = "b1be2855ed9ed8eac54e5caff2afcdb442d52c23"
uuid = "ea10d353-3f73-51f8-a26c-33c1cb351aa5"
version = "1.4.2"

[[deps.Widgets]]
deps = ["Colors", "Dates", "Observables", "OrderedCollections"]
git-tree-sha1 = "505c31f585405fc375d99d02588f6ceaba791241"
uuid = "cc8bc4a8-27d6-5769-a93b-9d913e69aa62"
version = "0.6.5"

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

[[deps.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"

[[deps.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"

[[deps.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"

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

[[deps.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"

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

[[deps.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"

[[deps.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"

[[deps.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"

[[deps.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"

[[deps.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"

[[deps.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"

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

[[deps.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"

[[deps.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"

[[deps.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"

[[deps.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"

[[deps.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"

[[deps.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"

[[deps.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"

[[deps.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"

[[deps.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"

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

[[deps.Zlib_jll]]
deps = ["Libdl"]
uuid = "83775a58-1f1d-513f-b197-d71354ab007a"
version = "1.2.12+3"

[[deps.Zstd_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "e45044cd873ded54b6a5bac0eb5c971392cf1927"
uuid = "3161d3a3-bdf6-5164-811a-617609db77b4"
version = "1.5.2+0"

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

[[deps.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"

[[deps.libblastrampoline_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "8e850b90-86db-534c-a0d3-1478176c7d93"
version = "5.1.0+0"

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

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

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

[[deps.nghttp2_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "8e850ede-7688-5339-a07c-302acd2aaf8d"
version = "1.41.0+1"

[[deps.p7zip_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "3f19e933-33d8-53b3-aaab-bd5110c3b7a0"
version = "16.2.1+1"

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

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

[[deps.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:
# ╠═95965ab2-f250-479f-9d5d-e478dba1fe35
# ╠═4458903f-4717-4603-a707-4d2fd587470b
# ╠═d577b8c8-3670-497a-a6fe-41208a8e8501
# ╠═90028541-7308-476f-b51b-850cd6ad39c4
# ╟─1217e4ab-8e97-4b73-9493-a58c7d8165fe
# ╟─100c3470-b7e4-4890-9347-851b78f5202f
# ╟─464ddfd5-d06b-4615-bd23-e63e03a29f1e
# ╠═fe81bd6a-c7bf-437d-8ca6-f21f9b45b41f
# ╟─b6c8f7af-8e39-4792-a62c-88a41876345d
# ╠═8ee2eec3-3214-48d1-8604-a54ba1a67baf
# ╟─573253a5-10d4-458e-9451-89c763658810
# ╠═fa9dff6f-3182-4093-bbfd-8deea404eab0
# ╟─2367f3cf-c568-4f6c-82c6-b7ae42408404
# ╠═8185285a-1640-45e9-8c80-b17b6c960804
# ╟─40634f53-8104-4791-877c-2d498cab9570
# ╠═885a0261-3541-4389-beb7-231c77e2dfcc
# ╟─6837fff8-0c29-4ba1-9b3b-b21c23d861eb
# ╠═1f30d601-4e00-44dd-a6ab-363c431ca875
# ╠═de06a783-c2ff-4f45-8a1e-02977ad31e26
# ╟─30be727e-86e6-41cf-be58-e0b1ffb372c2
# ╠═5ca07e4a-bf45-4e3c-9a5b-3b9b7af38020
# ╟─f95ec79a-0263-46e4-b82e-a274cb7ee7fb
# ╟─81f57cdb-36f8-43bb-86a5-19bac5cd88b1
# ╠═78fe51f6-beea-4155-905d-2d5e6e7d66d7
# ╟─4ea3a429-e457-48a1-a66a-ea66ff21d22c
# ╠═8bb5afba-3f59-4776-9a7b-8df9fed58a90
# ╟─5188efaa-8a5e-4fac-9e7f-bf048079ab9c
# ╠═23810d4f-1dd6-4c16-bf71-231b8b4b726d
# ╟─91780708-0829-4beb-8144-7fc5b7e76b3f
# ╠═cdeba577-a184-4bb5-97a9-6acf3ff516a3
# ╟─e049f64c-02e0-4087-b341-eaf437c5ba49
# ╟─687aec56-682c-4153-ac35-58926c03ea26
# ╠═0c918f86-e896-4b19-8cf8-a77203c3a61b
# ╠═fee0f70c-9aa5-4b60-a285-6923fedbd06c
# ╠═57050894-2fcb-48e0-bd41-14502da1b5ae
# ╟─2a1dd0cf-5a09-43bd-b7bf-5c93bea3bf3b
# ╠═d15e5041-6021-483e-b059-7170077c2ea6
# ╟─425eea72-221d-4990-90f2-a6654f4e98e1
# ╠═ccc7d18c-08ed-41a7-a556-26030a19d6c5
# ╟─6b73a8a5-c542-4a10-8cf1-0a7e40c3cc98
# ╠═bc41a9ab-c960-4d17-9782-f01721337aea
# ╟─40ec9daa-913e-4b2c-a0aa-3e70a2de7c71
# ╠═b938e63c-29b1-4e49-90af-f9b2ab2e5bdd
# ╟─e5428608-cfc2-4fb0-873d-9a4944fb27f6
# ╟─0d6baf1d-2e2a-4742-944a-072bbd24b628
# ╠═ef730308-7bf8-489a-9ab5-a869efe6083a
# ╠═1c4b4cb8-12c0-4fb3-8523-062c7028f746
# ╠═9610477f-8311-4cbf-8544-b9f4836926d6
# ╠═e5216885-c156-4454-ac96-eed454435695
# ╠═6e47526a-310a-4a3e-aab5-0fe71c6c7814
# ╟─944c59b8-ecf6-4ec3-9e81-7ffb8692db36
# ╟─233cd90e-463d-49fb-9a54-34e2750c2a8c
# ╠═b28587b9-5e60-42b0-9874-d47b3e03b97c
# ╟─4fb1f19d-2802-4a0f-bb35-1e21c0be68f3
# ╠═aad09fb4-1fee-454f-bdad-65b2a93255ca
# ╠═0d451930-833e-4050-b2f9-d5f997fb0098
# ╟─3878adef-0d96-4e73-ab37-4e761e01e0ac
# ╠═500fb09f-f952-46a0-8d63-98279e630882
# ╠═95d072b9-5940-49ce-97a8-8dde13c25939
# ╟─1f3d5631-8261-4c3b-8e34-761d23eb5e2e
# ╠═a856d989-5fb6-4148-ac7d-2ce52952c1a3
# ╠═9a7ebb96-5ce1-4093-8c85-9522edebab0e
# ╠═48d158ed-a25f-4ebe-8863-6c92071c251c
# ╟─199ae6d5-7306-4802-bd18-4232fdb98f5f
# ╠═aee19854-5c3d-4a9e-8639-91843800d1b6
# ╟─e01fa7a9-16ac-498e-97d3-8c9fe1255f43
# ╟─48fe8dff-dc91-4996-bfe7-911d2a09b4c8
# ╠═aef2347f-dea0-4bbb-864c-c7d0d09814c6
# ╟─011c2852-91b3-4745-b453-e0ffcdba7f23
# ╟─6916ba32-8ebc-4aa7-adf7-f6717fde60e2
# ╠═afaf9be1-a557-4b73-9279-f9cf12525958
# ╟─1c03fd5e-0c6a-4118-b11a-0f4d2392f923
# ╠═1cd43a15-d361-4e4a-84e2-f1464659a654
# ╠═2be10e8e-9a44-4b0b-bd81-7e4cdc999afc
# ╠═ee84ac32-58f1-49bc-b705-fbc709e0f11a
# ╠═8448e4cd-0bce-4426-85db-72a40a279b1d
# ╠═640ac000-dd55-4dda-846f-303404360ab5
# ╠═038bc011-279e-492a-bbfc-074630cdff3e
# ╠═c8d7399e-ad0d-4835-8fa0-1c8ad66e7d34
# ╠═1512c0e0-bee0-4fce-9062-39c60e43f3f8
# ╠═93a5e590-0ab0-4a13-8944-226258424f7d
# ╟─aba1a47c-534b-4ce0-b41f-d68c3331207d
# ╠═2ff1b0f7-4a07-467f-bf0d-069c5b766ed1
# ╟─0f77c94d-011e-4a55-99a1-0ee67acf63fb
# ╟─00000000-0000-0000-0000-000000000001
# ╟─00000000-0000-0000-0000-000000000002
