Random variate transformations in the Gibbs sampler: issues of efficiency and convergence

Abstract

In the non-conjugate Gibbs sampler, the required sampling from the full conditional densities needs the adoption of black-box sampling methods. Recent suggestions include rejection sampling, adaptive rejection sampling, generalized ratio of uniforms, and the Griddy-Gibbs sampler. This paper describes a general idea based on variate transformations which can be tailored in all the above methods and increase the Gibbs sampler efficiency. Moreover, a simple technique to assess convergence is suggested and illustrative examples are presented.

An Approach to Diagnosing Total Variation Convergence of MCMC Algorithms

“…Assuming the following priors, see Diebolt and Robert (1994). Note that because gt = a;, we use the non-normalized density in Equation (5.1).…”