HAAR-WEAVE-METROPOLIS KERNEL

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Abstract

Recently, many Markov chain Monte Carlo methods have been developed with deterministic reversible transform proposals inspired by the Hamiltonian Monte Carlo method. The deterministic transform is relatively easy to reconcile with the local information (gradient etc.) of the target distribution. However, as the ergodic theory suggests, these deterministic proposal methods seem to be incompatible with robustness and lead to poor convergence, especially in the case of target distributions with heavy tails. On the other hand, the Markov kernel using the Haar measure is relatively robust since it learns global information about the target distribution introducing global parameters. However, it requires a density preserving condition, and many deterministic proposals break this condition. In this paper, we carefully select deterministic transforms that preserve the value of the density function and create a Markov kernel, the Weave-Metropolis kernel, using the deterministic transforms. By combining with the Haar measure, we also introduce the Haar-Weave-Metropolis kernel. In this way, the Markov kernel can employ the local information of the target distribution using the deterministic proposal, and thanks to the Haar measure, it can employ the global information of the target distribution. Finally, we show through numerical experiments that the performance of the proposed method is superior to other methods in terms of effective sample size and mean square jump distance per second.

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Details 詳細情報について

  • CRID
    1390573242447673728
  • NII Article ID
    120007193399
  • NII Book ID
    AA10634475
  • DOI
    10.5109/4755997
  • ISSN
    2435743X
    0286522X
  • HANDLE
    2324/4755997
  • Text Lang
    en
  • Data Source
    • JaLC
    • IRDB
    • Crossref
    • CiNii Articles
    • KAKEN
  • Abstract License Flag
    Allowed

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