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Shen, Xiaotong; Wasserman, Larry

Rates of convergence of posterior distributions. (English) Zbl 1041.62022

Ann. Stat. 29, No. 3, 687-714 (2001).
Summary: 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 measured by bracketing entropy, and the degree to which the prior concentrates in a small ball around the true parameter. We consider two examples.

Cited in 118 Documents

MSC:

62F15 Bayesian inference
62E20 Asymptotic distribution theory in statistics
62G20 Asymptotic properties of nonparametric inference

Keywords:

asymptotic inference; sieves
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References:

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