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 in finite dimensional cases. The rates are driven by two quantities: the size of the space, as measured by bracketing entropy, and the degree to which the prior concentrates in a small ball around the true parameter. We consider two examples.
"Rates of convergence of posterior distributions." Ann. Statist. 29 (3) 687 - 714, June 2001. https://doi.org/10.1214/aos/1009210686