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Algorithms for improving efficiency of discrete Markov chains

Author

Listed:
  • Nabanita Mukherjee

    (Duke University)

  • George Casella

    (University of Florida)

  • Kshitij Khare

    (University of Florida)

Abstract

Sampling from an intractable probability distribution is a common and important problem in scientific computing. A popular approach to solve this problem is to construct a Markov chain which converges to the desired probability distribution, and run this Markov chain to obtain an approximate sample. In this paper, we provide two methods to improve the performance of a given discrete reversible Markov chain. These methods require the knowledge of the stationary distribution only up to a normalizing constant. Each of these methods produces a reversible Markov chain which has the same stationary distribution as the original chain, and dominates the original chain in the ordering introduced by Peskun [11]. We illustrate these methods on two Markov chains, one connected to hidden Markov models and one connected to card shuffling. We also prove a result which shows that the Metropolis-Hastings algorithm preserves the Peskun ordering for Markov transition matrices.

Suggested Citation

  • Nabanita Mukherjee & George Casella & Kshitij Khare, 2017. "Algorithms for improving efficiency of discrete Markov chains," Indian Journal of Pure and Applied Mathematics, Springer, vol. 48(4), pages 495-511, December.
    • Handle: RePEc:spr:indpam:v:48:y:2017:i:4:d:10.1007_s13226-017-0242-7
    DOI: 10.1007/s13226-017-0242-7
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