Convergence rates of posterior distributions for noniid observations

• 成果类型: Article
• 署名作者: Ghosal, Subhashis; Van Der Vaart, Aad
• 署名单位: North Carolina State University; Vrije Universiteit Amsterdam
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/009053606000001172
• 发表日期: 2007
• 页码: 192-223
• 关键词: time-series; nonparametric problems; bernstein polynomials; maximum-likelihood; DENSITY-ESTIMATION; Consistency; models

摘要

We consider the asymptotic behavior of posterior distributions and Bayes estimators based on observations which are required to be neither independent nor identically distributed. We give general results on the rate of convergence of the posterior measure relative to distances derived from a testing criterion. We then specialize our results to independent, nonidentically distributed observations, Markov processes, stationary Gaussian time series and the white noise model. We apply our general results to several examples of infinite-dimensional statistical models including nonparametric regression with normal errors, binary regression, Poisson regression, an interval censoring model, Whittle estimation of the spectral density of a time series and a nonlinear autoregressive model.