Small-world MCMC and convergence to multi-modal distributions: From slow mixing to fast mixing

Journal Article (Journal Article)

We compare convergence rates of Metropolis-Hastings chains to multimodal target distributions when the proposal distributions can be of "local" and "small world" type. In particular, we show that by adding occasional long-range jumps to a given local proposal distribution, one can turn a chain that is "slowly mixing" (in the complexity of the problem.) into a chain that is "rapidly mixing." To do this, we obtain spectral gap estimates via a new state decomposition theorem and apply an isoperimetric inequality for log-concave probability measures. We discuss potential applicability of our result to Metropolis-coupled Markov chain Monte Carlo schemes. © Institute of Mathematical Statistics, 2007.

Full Text

Duke Authors

Cited Authors

  • Guan, Y; Krone, SM

Published Date

  • February 1, 2007

Published In

Volume / Issue

  • 17 / 1

Start / End Page

  • 284 - 304

Electronic International Standard Serial Number (EISSN)

  • 1050-5164

International Standard Serial Number (ISSN)

  • 1050-5164

Digital Object Identifier (DOI)

  • 10.1214/105051606000000772

Citation Source

  • Scopus