A Bayesian bootstrap for finite state Markov chains

Cheng Der Fuh, Tsai Hung Fan

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

The Bayesian bootstrap for Markov chains is the Bayesian analogue of the bootstrap method for Markov chains. We construct a random-weighted empirical distribution, based on i.i.d. exponential random variables, to simulate the posterior distribution of the transition probability, the stationary probability, as well as the first hitting time up to a specific state, of a finite state ergodic Markov chain. The large sample theory is developed which shows that with a matrix beta prior on the transition probability, the Bayesian bootstrap procedure is second-order consistent for approximating the pivot of the posterior distributions of the transition probability. The small sample properties of the Bayesian bootstrap are also discussed by a simulation study.

Original languageEnglish
Pages (from-to)1005-1019
Number of pages15
JournalStatistica Sinica
Volume7
Issue number4
StatePublished - Oct 1997

Keywords

  • Bayesian bootstrap
  • Hitting time
  • Markov chain
  • Matrix beta distribution
  • Transition probability

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