text:
### 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
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[compat]
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Turing = "~0.21.1"
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deps = ["Adapt", "DiffRules", "ForwardDiff", "LinearAlgebra", "LogExpFunctions", "MacroTools", "NNlib", "NaNMath", "Printf", "Random", "Requires", "SpecialFunctions", "Statistics"]
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version = "0.2.20"

[[deps.TranscodingStreams]]
deps = ["Random", "Test"]
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[[deps.Transducers]]
deps = ["Adapt", "ArgCheck", "BangBang", "Baselet", "CompositionsBase", "DefineSingletons", "Distributed", "InitialValues", "Logging", "Markdown", "MicroCollections", "Requires", "Setfield", "SplittablesBase", "Tables"]
git-tree-sha1 = "c76399a3bbe6f5a88faa33c8f8a65aa631d95013"
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[[deps.TreeViews]]
deps = ["Test"]
git-tree-sha1 = "8d0d7a3fe2f30d6a7f833a5f19f7c7a5b396eae6"
uuid = "a2a6695c-b41b-5b7d-aed9-dbfdeacea5d7"
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[[deps.Tullio]]
deps = ["ChainRulesCore", "DiffRules", "LinearAlgebra", "Requires"]
git-tree-sha1 = "859e2e9a7222553a0c052e423557cedb49376da9"
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[[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"
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[[deps.UUIDs]]
deps = ["Random", "SHA"]
uuid = "cf7118a7-6976-5b1a-9a39-7adc72f591a4"

[[deps.UnPack]]
git-tree-sha1 = "387c1f73762231e86e0c9c5443ce3b4a0a9a0c2b"
uuid = "3a884ed6-31ef-47d7-9d2a-63182c4928ed"
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[[deps.Unicode]]
uuid = "4ec0a83e-493e-50e2-b9ac-8f72acf5a8f5"

[[deps.UnicodeFun]]
deps = ["REPL"]
git-tree-sha1 = "53915e50200959667e78a92a418594b428dffddf"
uuid = "1cfade01-22cf-5700-b092-accc4b62d6e1"
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[[deps.Unzip]]
git-tree-sha1 = "34db80951901073501137bdbc3d5a8e7bbd06670"
uuid = "41fe7b60-77ed-43a1-b4f0-825fd5a5650d"
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[[deps.VectorizationBase]]
deps = ["ArrayInterface", "CPUSummary", "HostCPUFeatures", "Hwloc", "IfElse", "LayoutPointers", "Libdl", "LinearAlgebra", "SIMDTypes", "Static"]
git-tree-sha1 = "ff34c2f1d80ccb4f359df43ed65d6f90cb70b323"
uuid = "3d5dd08c-fd9d-11e8-17fa-ed2836048c2f"
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[[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:
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text:
const checker_width_dialog = Dialog()
const checker_per_width_dialog = Dialog()
const checker_per_height_dialog = Dialog()

function newboard(designations)
    @label desig
    dialog = Dialog()
    examples = isempty(designations) ? "" : "(already existing designations: $designations) "
    designation = request("Give a designation for this new board:$examples", dialog)
    if designation ∈ designations
        @warn "designation $designation is already taken, try again…"
        @goto desig
    end
    isempty(designation) && @goto desig
    @label width
    _checker_width_cm = requestᵐ("What is the width (same as height) of the checkers in cm?", checker_width_dialog)
    if !all(isnumeric, filter(!isequal('.'), _checker_width_cm))
        @warn "width $_checker_width_cm is not a number, try again…"
        @goto width
    end
    checker_width_cm = parse(Float64, _checker_width_cm)
    if checker_width_cm < 0
        @warn "width $_checker_width_cm has to be larger than zero, try again…"
        @goto width
    end
    @label perwidth
    _checker_per_width = requestᵐ("How many checkers are there across the width of the board?", checker_per_width_dialog)
    if !all(isnumeric, _checker_per_width)
        @warn "$_checker_per_width is not an integer, try again…"
        @goto perwidth
    end
    checker_per_width = parse(Int, _checker_per_width)
    if checker_per_width < 1
        @warn "there has to be more than one checkers, try again…"
        @goto perwidth
    end
    @label perheight
    _checker_per_height = requestᵐ("How many checkers are there across the height of the board?", checker_per_height_dialog)
    if !all(isnumeric, _checker_per_height)
        @warn "$_checker_per_height is not an integer, try again…"
        @goto perheight
    end
    checker_per_height = parse(Int, _checker_per_height)
    if checker_per_height < 1
        @warn "there has to be more than one checkers, try again…"
        @goto perheight
    end
    @label describe
    dialog = Dialog()
    board_description = request("""Describe the board to facilitate recognizing it in the future (e.g. "a small board, black tape framming it on the long side, cardboard on the short"):""", dialog)
    if isempty(board_description)
        @warn "you must give some minimal description. Think about the future generations!"
        @goto describe
    end
    try
        Board(designation, checker_width_cm, (checker_per_width, checker_per_height), board_description)
    catch ex
        @warn "something was wrong" ex
        @goto desig
    end
end

const calibration_type_menu = RadioMenu(["Stationary", "Moving"])
const calibration_comment_dialog = Dialog()

function newcalibration(boards)
    board = if isempty(boards)
        @info "registering a new board"
        newboard(String[])
    else
        designations = getfield.(boards, :designation)
        options = designations
        pushfirst!(options, "Register a new board")
        board_menu = RadioMenu(options, min(2, length(options)))
        i = requestᵐ("Which board was used?", board_menu)
        i == 1 ? newboard(designations) : boards[i - 1]
    end

    @label newcalibl

    i = requestᵐ("Which type of calibration is it?", calibration_type_menu)
    intrinsic = if i == 1
        missing
    else
        println("Registrating the intrinsic calibration POI (waving the checkerboard around)")
        newinterval(true)
    end
    println("Registrating the extrinsic calibration POI (the checkerboard on the ground)")
    extrinsic = newinterval(false)

    comment = requestᵐ("Any comments about this calibration?", calibration_comment_dialog)
    try
        Calibration(intrinsic, extrinsic, board, comment)
    catch ex
        @warn "something was wrong" ex
        @goto newcalibl
    end
end

ext: jl


text:
using DifferentialEquations
using LinearAlgebra
using Random
using Statistics
using Plots

include("models/Vibron.jl")
include("modules/ClassicalDynamics.jl")

vibronParameters = [0.5,0.5,0.5]
energy = -0.5
numTrajectories = 10
PSPoints = 2000

initialCondition = [0.0, 0.1, missing, 0.1]
InitialCondition!(initialCondition, energy, vibronParameters)

#initialCondition = [0.0, 1.0203574072397172, -0.9189955424295329, 0.23490092884445612]

pyplot(size = (1800,1000))
Trajectory(initialCondition, vibronParameters)

max_stars_repo_name: PavelStransky/ClassicalDynamics

max_issues_repo_name: PavelStransky/ClassicalDynamics

max_forks_repo_name: PavelStransky/ClassicalDynamics


text:
using AbstractTrees
using Test

include(joinpath(@__DIR__,"examples","idtree.jl"))

@testset "IDTree" begin
    tree = IDTree(1 => [
        2 => [
            3,
            4 => [5],
        ],
        6,
        7 => [
            8 => [
                9,
                10,
                11 => 12:14,
                15,
            ],
        ],
        16,
    ])

    nodes = [tree.nodes[id] for id in 1:16]

    # Node/subtree properties
    #                              1   2  3  4  5  6  7  8  9 10 11 12 13 14 15 16
    @test treesize.(nodes)    == [16, 4, 1, 2, 1, 1, 9, 8, 1, 1, 4, 1, 1, 1, 1, 1]
    @test treebreadth.(nodes) == [10, 2, 1, 1, 1, 1, 6, 6, 1, 1, 3, 1, 1, 1, 1, 1]
    @test treeheight.(nodes)  == [ 4, 2, 0, 1, 0, 0, 3, 2, 0, 0, 1, 0, 0, 0, 0, 0]

    # Child/descendant checking
    @test ischild(nodes[2], nodes[1])
    @test ischild(nodes[3], nodes[2])
    @test !ischild(nodes[3], nodes[1])
    @test !ischild(nodes[1], nodes[2])
    @test !ischild("foo", nodes[1])
    @test !ischild(nodes[1], "foo")

    @test isdescendant(nodes[2], nodes[1])
    @test isdescendant(nodes[9], nodes[1])
    @test isdescendant(nodes[12], nodes[7])
    @test !isdescendant(nodes[1], nodes[2])
    @test !isdescendant(nodes[4], nodes[8])
    @test !isdescendant(nodes[1], nodes[1])
    @test !isdescendant("foo", nodes[1])
    @test !isdescendant(nodes[1], "foo")

    @test intree(nodes[2], nodes[1])
    @test intree(nodes[9], nodes[1])
    @test intree(nodes[12], nodes[7])
    @test !intree(nodes[1], nodes[2])
    @test !intree(nodes[4], nodes[8])
    @test intree(nodes[1], nodes[1])
    @test !intree("foo", nodes[1])
    @test !intree(nodes[1], "foo")

    # Traversal
    @test [n.id for n in PreOrderDFS(tree.root)] == 1:16
    @test [n.id for n in PostOrderDFS(tree.root)] == [3, 5, 4, 2, 6, 9, 10, 12, 13, 14, 11, 15, 8, 7, 16, 1]
    @test [n.id for n in Leaves(tree.root)] == [3, 5, 6, 9, 10, 12, 13, 14, 15, 16]
end

include(joinpath(@__DIR__,"examples","onenode.jl"))

@testset "OneNode" begin
    ot = OneNode([2,3,4,0], 1)
    @inferred collect(Leaves(ot))
    @test nodevalue.(collect(Leaves(ot))) == [0]
    @test eltype(nodevalue.(collect(Leaves(ot)))) ≡ Int
    @test nodevalue.(collect(PreOrderDFS(ot))) == [2,3,4,0]
    @test nodevalue.(collect(PostOrderDFS(ot))) == [0,4,3,2]
end

include(joinpath(@__DIR__,"examples","onetree.jl"))

@testset "OneTree" begin
    ot = OneTree([2,3,4,0])
    n = IndexNode(ot)

    @inferred collect(Leaves(n))
    @test nodevalue.(collect(Leaves(n))) == [0]
    @test eltype(nodevalue.(collect(Leaves(n)))) ≡ Int
    @test nodevalue.(collect(PreOrderDFS(n))) == [2,3,4,0]
    @test nodevalue.(collect(PostOrderDFS(n))) == [0,4,3,2]
end

include(joinpath(@__DIR__,"examples","fstree.jl"))

@testset "FSNode" begin
    mk_tree_test_dir() do path
        tree = Directory(".")

        ls = nodevalue.((collect ∘ Leaves)(tree))
        # use set so we don't have to guarantee ordering
        @test Set(ls) == Set([joinpath(".","A","f2"), joinpath(".","B"), joinpath(".","f1")])
        @test treeheight(tree) == 2
    end
end

include(joinpath(@__DIR__,"examples","binarytree.jl"))

@testset "BinaryNode" begin
    t = binarynode_example()

    ls = @inferred collect(Leaves(t))
    @test nodevalue.(ls) == [3, 2]

    predfs = @inferred collect(PreOrderDFS(t))
    @test nodevalue.(predfs) == [0,1,3,2]

    postdfs = @inferred collect(PostOrderDFS(t))
    @test nodevalue.(postdfs) == [3,1,2,0]

    sbfs = @inferred collect(StatelessBFS(t))
    @test nodevalue.(sbfs) == [0,1,2,3]
end