using StatisticalRethinking

In Rethinking the model actually has priors that are U[-Inf, Inf], or as the Stan manual (2.17.0, pp. 127) tells us:

"A parameter declared without constraints is thus given a uniform prior on (−∞, ∞) ..."

But setting -Inf and Inf in Turing doesn't work. So the below works of course better since we've restrained it to [-1,1]

@model m8_2(y) = begin
    σ ~ Uniform(-1, 1)
    α ~ Uniform(-1, 1)

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

y = [-1,1]

posterior = sample(m8_2(y), Turing.NUTS(4000, 1000, 0.95))
describe(posterior)

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