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February 1996 Locally uniform prior distributions
J. A. Hartigan
Ann. Statist. 24(1): 160-173 (February 1996). DOI: 10.1214/aos/1033066204


Suppose that $X_{\sigma} | \mathbf{\theta} \sim N(\mathbf{\theta}, \sigma^2)$ and that $\sigma \to 0$. For which prior distributions on $\mathbf{\theta}$ is the posterior distribution of $\mathbf{\theta}$ given $X_{\sigma}$ asymptotically $N(X_{\sigma}, \sigma^2)$ when in fact $X_{\sigma} \sim N(\theta_0, \sigma^2)$? It is well known that the stated convergence occurs when $\mathbf{\theta}$ has a prior density that is positive and continuous at $\theta_0$. It turns out that the necessary and sufficient conditions for convergence allow a wider class of prior distributions--the locally uniform and tail-bounded prior distributions. This class includes certain discrete prior distributions that may be used to reproduce minimum description length approaches to estimation and model selection.


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J. A. Hartigan. "Locally uniform prior distributions." Ann. Statist. 24 (1) 160 - 173, February 1996.


Published: February 1996
First available in Project Euclid: 26 September 2002

zbMATH: 0853.62008
MathSciNet: MR1389885
Digital Object Identifier: 10.1214/aos/1033066204

Primary: 62A15

Keywords: Discrete prior distributions , minimum description length , penalized likelihood

Rights: Copyright © 1996 Institute of Mathematical Statistics

Vol.24 • No. 1 • February 1996
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