Convergence rates of posterior distributions for noniid observations

Details Convergence rates of posterior distributions for noniid observations Convergence rates of posterior distributions for noniid observations

2007-08-03

arxiv.org/abs/0708.0491v1

Annals of Statistics 2007, Vol. 35, No. 1, 192-223

Mathematics

Statistics Theory

Published at http://dx.doi.org/10.1214/009053606000001172 in the Annals of Statistics (http://www.imstat.org/aos/) by the Inst

Scientific paper

10.1214/009053606000001172

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.

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