### A Pluto.jl notebook ###
# v0.19.14

using Markdown
using InteractiveUtils

# ╔═╡ add4bb20-1da8-45e7-a40f-1b41c149d5f0
using Turing,StatsFuns, Distributions,StatsPlots,FillArrays

# ╔═╡ c39be064-648a-11ed-0677-ebe624104c69
md"""
# Model Description

s: Completion status
t: time remaining
τ: Time elapsed
x₁: current status
x₂: market competitors
x₃: other value (placeholder)

p,μ,σ = f(τ,X)
A,B = f(μ,σ)
(s,t) ~ (bernoulli(p), Gamma(A,B))
"""

# ╔═╡ fb1ce990-915e-46eb-88a6-ac3c2bc55f4e
begin #test params
	n = 100
end

# ╔═╡ a84568ec-f443-4b36-83ba-baf5aceae209
function dummy_builder(x)
	features = unique(x)
	z = zeros(Int,(length(x),length(features)))
	for (i,item) in enumerate(x), (j,feature) in enumerate(features)
		if item == feature
			z[i,j] = 1
		end
	end
	z
end

# ╔═╡ d75ac31e-9524-4ad7-b350-0a6dabdf22d2
begin
	τ = rand(Exponential(2),n)
	status = rand(["active","not recruiting","suspended"],n)
	x₁ = dummy_builder(status)
	x₂ = rand([0 1 2 3 4],n)
	x₃ = rand([1 2 3],n)

	X = hcat(τ, x₁, x₂, x₃)
end

# ╔═╡ 8735884f-efdc-4421-a205-06b68946b564
begin #build statuses
	ξ = [-5 6 -7 3 -2 4]'
	Ξ = logistic.(X * ξ)
	s = rand.(Bernoulli.(Ξ))
end

# ╔═╡ 7cee4dad-17b4-4cf8-8fa7-631722c4f9bf
begin #Build Durations
	β = [1 2 3 4 5 1]'
	ν = [6 5 4 3 2 1]'
	α = [-1,1] 

	
	μ = X * β .+ [α[x+1] for x in s]
	η = (X * ν).^2


	t = rand.(Normal.(μ,η))
end

# ╔═╡ f0687986-ac5f-47c7-ad79-07318d770d17
plot(Ξ,s,seriestype=:scatter, legend=nothing)

# ╔═╡ fd7264ce-00af-49a3-91c9-2277bad2b3e9
@model function MultiVariate(s,t,X)
	n,k=size(X)

	#model S
	ξ ~ MvNormal(zeros(k),2)
	σₛ ~ Exponential(1)

	μ = X*ξ
	p = logistic.(μ)

	s .~ Bernoulli.(p)
	
	#model t
	β ~ MvNormal(zeros(k),2)
	ν ~ MvNormal(zeros(k),2)
	α ~ MvNormal([0,0], 2)
	
	μ = X * β .+ [α[x+1] for x in s]
	η = (X * ν).^2


	t .~ Normal.(μ,η)
end

# ╔═╡ a9362616-b992-4100-b000-48c8ae7b4d4b
a =[1,2]

# ╔═╡ edad9362-fbd3-445a-857d-9687c1adbddd
testmod = MultiVariate(s,t,X)

# ╔═╡ d30d54df-260e-4826-89e3-de5434f8a730
chain = sample(testmod,Gibbs(NUTS(),PG(20,:α)),1000)

# ╔═╡ 846a1840-5734-4ed3-9d9c-01f063cd0057
plot(chain)

# ╔═╡ 00000000-0000-0000-0000-000000000001
PLUTO_PROJECT_TOML_CONTENTS = """
[deps]
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Turing = "fce5fe82-541a-59a6-adf8-730c64b5f9a0"

[compat]
Distributions = "~0.25.77"
FillArrays = "~0.13.5"
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StatsPlots = "~0.15.4"
Turing = "~0.22.0"
"""

# ╔═╡ 00000000-0000-0000-0000-000000000002
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[[deps.Unicode]]
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[[deps.UnicodeFun]]
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[[deps.XML2_jll]]
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[[deps.XSLT_jll]]
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git-tree-sha1 = "91844873c4085240b95e795f692c4cec4d805f8a"
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[[deps.Xorg_libX11_jll]]
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git-tree-sha1 = "5be649d550f3f4b95308bf0183b82e2582876527"
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[[deps.Xorg_libXau_jll]]
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uuid = "0c0b7dd1-d40b-584c-a123-a41640f87eec"
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[[deps.Xorg_libXcursor_jll]]
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git-tree-sha1 = "12e0eb3bc634fa2080c1c37fccf56f7c22989afd"
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[[deps.Xorg_libXi_jll]]
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git-tree-sha1 = "89b52bc2160aadc84d707093930ef0bffa641246"
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[[deps.Xorg_libXinerama_jll]]
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git-tree-sha1 = "26be8b1c342929259317d8b9f7b53bf2bb73b123"
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[[deps.Xorg_libXrandr_jll]]
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git-tree-sha1 = "34cea83cb726fb58f325887bf0612c6b3fb17631"
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[[deps.Xorg_libXrender_jll]]
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git-tree-sha1 = "19560f30fd49f4d4efbe7002a1037f8c43d43b96"
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[[deps.Xorg_libpthread_stubs_jll]]
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git-tree-sha1 = "6783737e45d3c59a4a4c4091f5f88cdcf0908cbb"
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[[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"
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[[deps.Xorg_libxkbfile_jll]]
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git-tree-sha1 = "926af861744212db0eb001d9e40b5d16292080b2"
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[[deps.Xorg_xcb_util_image_jll]]
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git-tree-sha1 = "0fab0a40349ba1cba2c1da699243396ff8e94b97"
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[[deps.Xorg_xcb_util_jll]]
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git-tree-sha1 = "e7fd7b2881fa2eaa72717420894d3938177862d1"
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[[deps.Xorg_xcb_util_keysyms_jll]]
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git-tree-sha1 = "d1151e2c45a544f32441a567d1690e701ec89b00"
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[[deps.Xorg_xcb_util_renderutil_jll]]
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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"
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[[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]]
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git-tree-sha1 = "79c31e7844f6ecf779705fbc12146eb190b7d845"
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[[deps.Zlib_jll]]
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[[deps.Zstd_jll]]
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git-tree-sha1 = "e45044cd873ded54b6a5bac0eb5c971392cf1927"
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git-tree-sha1 = "8c1a8e4dfacb1fd631745552c8db35d0deb09ea0"
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[[deps.fzf_jll]]
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git-tree-sha1 = "868e669ccb12ba16eaf50cb2957ee2ff61261c56"
uuid = "214eeab7-80f7-51ab-84ad-2988db7cef09"
version = "0.29.0+0"

[[deps.libaom_jll]]
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git-tree-sha1 = "3a2ea60308f0996d26f1e5354e10c24e9ef905d4"
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[[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"
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[[deps.libblastrampoline_jll]]
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uuid = "8e850b90-86db-534c-a0d3-1478176c7d93"
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[[deps.libfdk_aac_jll]]
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git-tree-sha1 = "daacc84a041563f965be61859a36e17c4e4fcd55"
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[[deps.libpng_jll]]
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git-tree-sha1 = "94d180a6d2b5e55e447e2d27a29ed04fe79eb30c"
uuid = "b53b4c65-9356-5827-b1ea-8c7a1a84506f"
version = "1.6.38+0"

[[deps.libvorbis_jll]]
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git-tree-sha1 = "b910cb81ef3fe6e78bf6acee440bda86fd6ae00c"
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[[deps.p7zip_jll]]
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uuid = "3f19e933-33d8-53b3-aaab-bd5110c3b7a0"
version = "17.4.0+0"

[[deps.x264_jll]]
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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 = "9ebfc140cc56e8c2156a15ceac2f0302e327ac0a"
uuid = "d8fb68d0-12a3-5cfd-a85a-d49703b185fd"
version = "1.4.1+0"
"""

# ╔═╡ Cell order:
# ╟─c39be064-648a-11ed-0677-ebe624104c69
# ╠═add4bb20-1da8-45e7-a40f-1b41c149d5f0
# ╠═fb1ce990-915e-46eb-88a6-ac3c2bc55f4e
# ╠═d75ac31e-9524-4ad7-b350-0a6dabdf22d2
# ╟─a84568ec-f443-4b36-83ba-baf5aceae209
# ╠═7cee4dad-17b4-4cf8-8fa7-631722c4f9bf
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