Comparison of hit-and-run, slice sampler and random walk Metropolis. (16th January 2019)

• Record Type: Journal Article
• Authors: Rudolf, Daniel; Ullrich, Mario
• Is Part Of: Journal of applied probability. Volume 55:Number 4(2018)
• Page Start: 1186
• Page End: 1202
• Publication Date: 2019-01-16
• Subjects: Hit-and-run, -- slice sampler, -- random walk Metropolis, -- covariance ordering; Primary 60J22, -- Secondary 65C05, -- 60J05; 519.2
• DOI: 10.1017/jpr.2018.78
• Languages: English
• ISSNs: 0021-9002

Abstract

Abstract: Different Markov chains can be used for approximate sampling of a distribution given by an unnormalized density function with respect to the Lebesgue measure. The hit-and-run, (hybrid) slice sampler, and random walk Metropolis algorithm are popular tools to simulate such Markov chains. We develop a general approach to compare the efficiency of these sampling procedures by the use of a partial ordering of their Markov operators, the covariance ordering. In particular, we show that the hit-and-run and the simple slice sampler are more efficient than a hybrid slice sampler based on hit-and-run, which, itself, is more efficient than a (lazy) random walk Metropolis algorithm.