Convergence Rates of Nonparametric Posterior Distributions

Details Convergence Rates of Nonparametric Posterior Distributions Convergence Rates of Nonparametric Posterior Distributions

2008-04-17

arxiv.org/abs/0804.2733v1

Mathematics

Statistics Theory

22 pages

Scientific paper

We study the asymptotic behavior of posterior distributions. We present general posterior convergence rate theorems, which extend several results on posterior convergence rates provided by Ghosal and Van der Vaart (2000), Shen and Wasserman (2001) and Walker, Lijor and Prunster (2007). Our main tools are the Hausdorff $\alpha$-entropy introduced by Xing and Ranneby (2008) and a new notion of prior concentration, which is a slight improvement of the usual prior concentration provided by Ghosal and Van der Vaart (2000). We apply our results to several statistical models.

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