ClinicalTrialsEstimation/Julia-turing models/Logistic_WorkingParamRecovery.jl

### A Pluto.jl notebook ###
# v0.19.19

using Markdown
using InteractiveUtils

# ╔═╡ c3854198-646b-11ed-1d90-077419a6a860
using Turing,StatsFuns,Distributions,StatsPlots,FillArrays

# ╔═╡ f6fc4578-43c5-4fb7-a24c-2567aa5b33c1
using Random

# ╔═╡ 735ae519-019e-48c6-8b73-7982fa60501a
md"""
This model is designed to recover parameters through logistic regression.

Note that recovery depends on specifying generating the data properly.
"""

# ╔═╡ bd9391b7-5240-46ca-be26-357292ffaddb
begin #creating synthetic data
	#n = 100_000 #successfully tested with n=100_000. It recovered the values quite well.
	n = 1000
	β = [1 2 -3]
	α = 0
	k=length(β)
	ϵ = randn(n)
	X = rand(Uniform(0,1),(n,k))

	B = α .+ (X*β')
	lB=logistic.(B)
	y = rand.(Bernoulli.(lB))
end

# ╔═╡ 9bf20953-ae30-4468-943a-ddc2898da9b3
maximum(B),minimum(B),mean(B),std(B)

# ╔═╡ 7fa29a18-6988-49b8-b2b4-b41a31de5757
histogram(B)

# ╔═╡ 9ea0c03d-65f5-41db-b455-299cb7461e51
plot(lB,y,seriestype=:scatter,legend=nothing)

# ╔═╡ 0696416b-72ba-46a0-ac54-0f8afbba554b
@model function Logit(y,X)
	n,k = size(X)
	β ~ MvNormal(zeros(k),1)
	σ ~ Exponential(1)
	α ~ Normal(0,1)

	μ = α .+ X*β
	p = logistic.(μ)

	y .~ Bernoulli.(p)
end

# ╔═╡ a2632230-b891-48b3-ba05-d34dc6076101
# ╠═╡ disabled = true
#=╠═╡
MvNormal(zeros(k),1)
  ╠═╡ =#

# ╔═╡ af054878-09ed-4c67-8655-5ff0bd0d1193
# ╠═╡ disabled = true
#=╠═╡
BernoulliLogit
  ╠═╡ =#

# ╔═╡ 3f4aa70d-ffce-44fe-8520-831a5a94fe47
testmodel = Logit(y,X)

# ╔═╡ 989b69de-e187-48f2-8454-8d86b232d895
chain = sample(testmodel,NUTS(),2000)

# ╔═╡ 8da7994b-ac63-4583-a360-d49cc8b04d35
plot(chain)

# ╔═╡ 00000000-0000-0000-0000-000000000001
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version = "1.4.1+0"
"""

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