期刊名称：Sankhya. Series A, mathematical statistics and probability
印刷版ISSN：0976-836X
电子版ISSN：0976-8378
出版年度：2015
卷号：77
期号：1
页码：106-125
DOI：10.1007/s13171-014-0055-2
语种：English
出版社：Indian Statistical Institute
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.
关键词：Nonparametric mixture ; Posterior consistency ; Transition density ; Markov process ; Martingale sequence.
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