Convergence rates of nonparametric posterior distributions

Abstract

We study the asymptotic behavior of posterior distributions. We present general posterior convergence rate theorems, which strengthen 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 and obtain some improvements on current results in these examples

Keywords

Hellinger consistency; posterior distribution; rate of convergence; sieve; infinite-dimensional model

Published in

Research report (Centre of Biostochastics)
2008, number: 7, pages: 1-27
Publisher: Centre of Biostochastics, SLU

SLU Authors

• Xing, Yang

  • Department of Forest Economics, Swedish University of Agricultural Sciences
    

Permanent link to this page (URI)

https://res.slu.se/id/publ/18931