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

共 19 条

[1]

Barndorff-Nielsen O.E., Sorensen M., A review of some aspects of asymptotic likelihood theory for stochastic processes, International Statistical Review, 62, 1, pp. 133-165, (1994)

[2]

Barron A., Schervish M.J., Wasserman L., The consistency of posterior distributions in nonparametric problems, The Annals of Statistics, 27, 2, pp. 536-561, (1999)

[3]

Beskos A., Papaspiliopoulos O., Roberts G.O., Fearnhead P., Exact and computationally efficient likelihood-based estimation for discretely observed diffusion processes (with discussion), Journal of the Royal Statistical Society, 68, 3, pp. 333-382, (2006)

[4]

Beskos A., Papaspiliopoulos O., Roberts G.O., Monte Carlo maximum likelihood estimation for discretely observed diffusion processes, The Annals of Statistics, 37, 1, pp. 223-245, (2009)

[5]

Bibby B.M., Sorensen M., Martingale estimation functions for discretely observed diffusion processes, Bernoulli, 1, 1-2, pp. 17-39, (1995)

[6]

Choi T., Schervish M.J., On posterior consistency in nonparametric regression problems, Journal of Multivariate Analysis, 98, pp. 1969-1987, (2007)

[7]

Ghosal S., Roy A., Consistency of Gaussian process prior for nonparametric binary regression, The Annals of Statistics, 34, 5, pp. 2413-2429, (2006)

[8]

Ghosal S., Tang Y., Bayesian consistency for Markov processes, The Indian Journal of Statistics, 68, 2, pp. 227-239, (2006)

[9]

Ghosal S., van der Vaart A., Convergence rates of posterior distributions for noniid observations, The Annals of Statistics, 35, 1, pp. 192-223, (2007)

[10]

Ghosal S., Ghosh J.K., Ramamoorthi R.V., Posterior consistency of Dirichlet mixtures in density estimation, The Annals of Statistics, 27, 1, pp. 143-158, (1999)

← 1 2 →