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Bayesian Consistency for Markov Models

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Abstract

We consider sufficient conditions for Bayesian consistency of the transition density of time homogeneous Markov processes. To date, this remains somewhat of an open problem, due to the lack of suitable metrics with which to work. Standard metrics seem inadequate, even for simple autoregressive models. Current results derive from generalizations of the i.i.d. case and additionally require some non-trivial model assumptions. We propose suitable neighborhoods with which to work and derive sufficient conditions for posterior consistency which can be applied in general settings. We illustrate the applicability of our result with some examples; in particular, we apply our result to a general family of nonparametric time series models.

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Authors and Affiliations

  1. Department of Decision Sciences, Bocconi University, Milan, MI, 20136, Italy

    Isadora Antoniano-Villalobos

  2. Department of Mathematics, University of Texas at Austin, Austin, Texas, 78712, U.S.A

    Stephen G. Walker

Authors
  1. Isadora Antoniano-Villalobos
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  2. Stephen G. Walker
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Correspondence to Isadora Antoniano-Villalobos.

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Antoniano-Villalobos, I., Walker, S.G. Bayesian Consistency for Markov Models. Sankhya A 77, 106–125 (2015). https://doi.org/10.1007/s13171-014-0055-2

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  • DOI: https://doi.org/10.1007/s13171-014-0055-2

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