using StatisticalRethinking

@model m8_3(y) = begin
    α ~ Normal(1, 10)
    σ ~ Truncated(Cauchy(0, 1), 0, Inf)

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

y = [-1,1]

posterior = sample(m8_3(y), Turing.NUTS(4000, 1000, 0.95))
describe(posterior)

        Mean          SD         Naive SE        MCSE         ESS

α -1.075811343 1.334041836 0.02109305348 0.19866042331 45.093733 σ 2.137823169 1.466095174 0.02318100009 0.18324552293 64.011438

According to Rethinking Mean StdDev lower 0.89 upper 0.89 n_eff Rhat alpha -0.01 1.60 -1.98 2.37 1121 1 sigma 1.98 1.91 0.47 3.45 1077 1

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