y, use of the <span class="math inline">\(\hat{R}\)</span> statistic makes very strong
assumptions. In particular, it assumes that the functions being
considered are Gaussian or it only uses the first two moments and
assumes some kind of independence. The point is that strong
assumptions are made that do not always hold. In particular, the
distribution for the log posterior density (<code>lp__</code>) almost
never looks Gaussian, instead it features long tails that can lead to
large <span class="math inline