Bayesian Consistency for Markov Models

被引：1

作者：

Antoniano-Villalobos I. ^{[1
]}

Walker S.G. ^{[2
]}

机构：

[1] Department of Decision Sciences, Bocconi University, Milan, 20136, MI

[2] Department of Mathematics, University of Texas at Austin, Austin, 78712, TX

来源：

Sankhya A | 2015年 / 77卷 / 1期

关键词：

Markov process; Martingale sequence; Nonparametric mixture; Posterior consistency; Transition density;

D O I：

10.1007/s13171-014-0055-2

中图分类号：

学科分类号：

摘要：

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. © 2014, Indian Statistical Institute.

引用

页码：106 / 125

页数：19

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