Bayesian estimation in multiple comparisons

Typical regression models do not automatically generate estimates for all the comparisons of a given factor F. Instead, a level is selected as a reference (i.e., intercept), and all other levels are estimated relative to said reference (i.e., slopes). While this situation is often aligned with our research questions and hypotheses, we sometimes wish to generate multiple comparisons involving different pairs of levels within F. This, however, is typically accompanied by p-value corrections or adjustments to minimize the rate of type I error. This paper shows how Bayesian hierarchical models can be used to generate multiple comparisons of entire posterior distributions. Crucially, these comparisons do not require adjustments.