Rates of Convergence of Posterior Distributions

Xiaotong Shen and Larry Wasserman


We compute the rate at which the posterior distribution concentrates around the true parameter value. The spaces we work in are quite general and include infinite dimensional cases. The rates are driven by two quantities: the size of the space, as measure by metric entropy or bracketing entropy, and the degree to which the prior concentrates in a small ball around the true parameter. We apply the results to several examples. In some cases, natural priors give sub-optimal rates of convergence and better rates can be obtained by using sieve-based priors.

AMS 1990 classification: Primary, 62A15, Secondary: 62E20, 62G15.

Keywords: Bayesian inference, asymptotic inference, non-parametric and semi-parametric models, sieves.

Here is the full postscript text for this technical report. It is 795798 bytes long.