= Non-centered Gaussian random-effect parameterization
{title2=$\alpha_i=\delta+\tau z_i,\quad z_i\sim N(0,1)$}
= Non-centred Gaussian random-effect parameterisation
{synonym}
A normal local effect $\alpha_i\mid\delta,\tau\sim N(\delta,\tau^2)$ can be represented by a standardized <latent variable> $z_i\sim N(0,1)$ independent of the hyperparameters, with $\alpha_i=\delta+\tau z_i$. This preserves the hierarchical model while changing the coordinates explored by <Markov chain Monte Carlo>. It often improves mixing when individual effects are weakly informed, reducing strong scale-effect dependence. Centered coordinates can be better with very informative individual data. The stochastic prior on $z_i$ implements the transformation correctly; re-expressing an existing density directly instead requires the appropriate <Jacobian determinant>.
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