using StatisticalRethinking
using Turing

Turing.setadbackend(:reverse_diff)

d = CSV.read(joinpath(dirname(Base.pathof(StatisticalRethinking)), "..", "data",
    "UCBadmit.csv"), delim=';')
size(d) # Should be 12x5

@model m11_5(admit, applications) = begin
    N=length(applications)
    θ ~ Truncated(Exponential(1), 0, Inf)
    α ~ Normal(0,2)

    for i ∈ 1:N
        prob = logistic(α)

alpha and beta for the BetaBinomial must be provided. The two parameterizations are related by alpha = prob * theta, and beta = (1-prob) * theta. See https://github.com/rmcelreath/rethinking/blob/master/man/dbetabinom.Rd

        alpha = prob * θ
        beta = (1 - prob) * θ

        admit[i] ~ BetaBinomial(applications[i], alpha, beta)
    end
end

posterior = sample(m11_5(d[:admit],d[:applications]), Turing.NUTS(4000, 1000, 0.9))
describe(posterior)

        Mean          SD         Naive SE         MCSE        ESS
   α  -0.372382104 0.3119992723 0.004933141643 0.00613870681 2583.1723
   θ   2.767996106 0.9897869845 0.015649906347 0.02305742759 1842.7303

Rethinking mean sd 5.5% 94.5% n_eff Rhat theta 2.74 0.96 1.43 4.37 3583 1 a -0.37 0.31 -0.87 0.12 3210 1

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