Multivariate-From-Univariate MCMC Sampler: The R Package MfUSampler

Abstract

The R package MfUSampler provides Markov chain Monte Carlo machinery for generating samples from multivariate probability distributions using univariate sampling algorithms such as the slice sampler and the adaptive rejection sampler. The multivariate wrapper performs a full cycle of univariate sampling steps, one coordinate at a time. In each step, the latest sample values obtained for other coordinates are used to form the conditional distributions. The concept is an extension of Gibbs sampling where each step involves, not an independent sample from the conditional distribution, but a Markov transition for which the conditional distribution is invariant. The software relies on proportionality of conditional distributions to the joint distribution to implement a thin wrapper for producing conditionals. Examples illustrate basic usage as well as methods for improving performance. By encapsulating the multivariate-from-univariate logic, package MfUSampler provides a reliable package for rapid prototyping of custom Bayesian models while allowing for incremental performance optimizations such as taking advantage of conditional independence, and high-performance implementation of function evaluations. Utility functions for MCMC diagnostics as well as sample-based construction of predictive posterior distributions are provided in MfUSampler.