  The R package MfUSampler provides Monte Carlo Markov Chain machinery for
generating samples from multivariate probability distributions using univariate
sampling algorithms such as Slice Sampler and Adaptive Rejection Sampler. The
sampler function 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, MfUSampler provides a reliable library for
rapid prototyping of custom Bayesian models while allowing for incremental
performance optimizations such as utilization of conjugacy, conditional
independence, and porting function evaluations to compiled languages.
