Open Access
2010 Reference priors for exponential families with increasing dimension
Bertrand Clarke, Subhashis Ghosal
Electron. J. Statist. 4: 737-780 (2010). DOI: 10.1214/10-EJS569


In this article, we establish the asymptotic normality of the posterior distribution for the natural parameter in an exponential family based on independent and identically distributed data. The mode of convergence is expected Kullback-Leibler distance and the number of parameters p is increasing with the sample size n. Using this, we give an asymptotic expansion of the Shannon mutual information valid when p=pn increases at a sufficiently slow rate. The second term in the asymptotic expansion is the largest term that depends on the prior and can be optimized to give Jeffreys’ prior as the reference prior in the absence of nuisance parameters. In the presence of nuisance parameters, we find an analogous result for each fixed value of the nuisance parameter. In three examples, we determine the rates at which pn can be allowed to increase while still retaining asymptotic normality and the reference prior property.


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Bertrand Clarke. Subhashis Ghosal. "Reference priors for exponential families with increasing dimension." Electron. J. Statist. 4 737 - 780, 2010.


Published: 2010
First available in Project Euclid: 17 August 2010

zbMATH: 1329.62120
MathSciNet: MR2678969
Digital Object Identifier: 10.1214/10-EJS569

Primary: 62F15
Secondary: 62C10

Keywords: exponential family , increasing dimension , mutual information , objective prior , posterior normality

Rights: Copyright © 2010 The Institute of Mathematical Statistics and the Bernoulli Society

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