= Latent-normal Gibbs sampler for probit regression
{title2=$Z_i\mid\beta\sim N(\beta x_i,1)$}
For binary observations with success probability $\Phi(\beta x_i)$, introduce latent $Z_i\sim N(\beta x_i,1)$ and let the sign determine the observation. Given $\beta$ and the observed sign, each latent variable has a <truncated normal distribution>. With a standard normal prior, the <full conditional distribution> of $\beta$ is normal with precision $1+\sum_i x_i^2$ and mean $\sum_i x_iZ_i/(1+\sum_i x_i^2)$. Alternating these blocks is <Gibbs sampling> with the required marginal posterior.
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