using StatisticalRethinking

Can't really set a U[-Inf,Inf] on \sigma AFAICT so this will not be 1:1 w/ Rethinking

@model m8_4(y) = begin
    α₁ ~ Uniform(-Inf, Inf)
    α₂ ~ Uniform(-Inf, Inf)
    σ ~ Truncated(Cauchy(0,1), 0, Inf)

    for i ∈ 1:length(y)
        y[i] ~ Normal(α₁ + α₂, σ)
    end
end

y = rand(Normal(0,1), 100)

posterior = sample(m8_4(y), Turing.NUTS(4000, 1000, 0.95))
describe(posterior)

Rethinking mean sd 5.5% 94.5% n_eff Rhat a1 -861.15 558.17 -1841.89 -31.04 7 1.43 a2 861.26 558.17 31.31 1842.00 7 1.43 sigma 0.97 0.07 0.89 1.09 9 1.17

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