xsample(): An R Function for Sampling Linear Inverse Problems

Abstract

An R function is implemented that uses Markov chain Monte Carlo (MCMC) algorithms to uniformly sample the feasible region of constrained linear problems. Two existing hit-and-run sampling algorithms are implemented, together with a new algorithm where an MCMC step reflects on the inequality constraints. The new algorithm is more robust compared to the hit-and-run methods, at a small cost of increased calculation time.