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Geometric Ergodicity and Scanning Strategies for Two-Component Gibbs Samplers

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  • Alicia A. Johnson
  • Owen Burbank

Abstract

In Markov chain Monte Carlo analysis, rapid convergence of the chain to its target distribution is crucial. A chain that converges geometrically quickly is geometrically ergodic. We explore geometric ergodicity for two-component Gibbs samplers (GS) that, under a chosen scanning strategy, evolve through one-at-a-time component-wise updates. We consider three such strategies: composition, random sequence, and random scans. We show that if any one of these scans produces a geometrically ergodic GS, so too do the others. Further, we provide a simple set of sufficient conditions for the geometric ergodicity of the GS. We illustrate our results using two examples.

Suggested Citation

  • Alicia A. Johnson & Owen Burbank, 2015. "Geometric Ergodicity and Scanning Strategies for Two-Component Gibbs Samplers," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 44(15), pages 3125-3145, August.
  • Handle: RePEc:taf:lstaxx:v:44:y:2015:i:15:p:3125-3145
    DOI: 10.1080/03610926.2013.823209
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