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Asymptotic normality of posterior distributions for exponential families when the number of parameters tends to infinity. (English) Zbl 1118.62309
Summary: We study consistency and asymptotic normality of posterior distributions of the natural parameter for an exponential family when the dimension of the parameter grows with the sample size. Under certain growth restrictions on the dimension, we show that the posterior distributions concentrate in neighborhoods of the true parameter and can be approximated by an appropriate normal distribution.

MSC:
62E20 Asymptotic distribution theory in statistics
62F15 Bayesian inference
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