Bayesian regression analysis using poly-t densities

Poly-t densities are defined by the property that their kernel is a product, or ratio of products, of Student-t kernels. These multivariate densities arise as Bayesian posterior densities for regression coefficients, under a surprising variety of specifications for the prior density and the data generating process. Although no analytical expression exists for the integrating constant and moments of these densities, these parameters are obtained through numerical integration in a number of dimensions given by the number of Student-t kernels in the numerator, minus one. The paper reviews how poly-t densities arise in regression analysis, and summarizes the results obtained for a number of models.