Convergence rates of posterior distributions for non-i.i.d. observations 论文

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.: θ ∈ Θ) be a sequence of statistical experiments with observations X (n), where the parameter set Θ is arbitrary and n is an indexing parameter, usually the sample size. We put a prior distribution Πn on θ ∈ Θ and study the rate of convergence of the posterior