Objective Priors: An Introduction for Frequentists

By Malay Ghosh. 2011

117 citations recorded by the source corpus.

Bayesian methods are increasingly applied in these days in the theory and practice of statistics. Any Bayesian inference depends on a likelihood and a prior. Ideally one would like to elicit a prior from related sources of information or past data. However, in its absence, Bayesian methods need to rely on some "objective" or "default" priors, and the resulting posterior inference can still be quite valuable. Not surprisingly, over the years, the catalog of objective priors also has become prohibitively large, and one has to set some specific criteria for the selection of such priors. Our aim is to review some of these criteria, compare their performance, and illustrate them with some simple examples. While for very large sample sizes, it does not possibly matter what objective prior one uses, the selection of such a prior does influence inference for small or moderate samples. For regular models where asymptotic normality holds, Jeffreys' general rule prior, the positive square root of the determinant of the Fisher information matrix, enjoys many optimality properties in the absence of nuisance parameters. In the presence of nuisance parameters, however, there are many other priors which emerge as optimal depending on the criterion selected. One new feature in this article is that a prior different from Jeffreys' is shown to be optimal under the chi-square divergence criterion even in the absence of nuisance parameters. The latter is also invariant under one-to-one reparameterization.

Subfields: Artificial Intelligence, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/1d60f3a98d106c787b4daa058d458df6cfd42631

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Citations in the corpus

Bayesian Estimation and Inference (2015, background): “Recent approaches with formalized rules for specifying uninformative priors for different types of distributions have been termed objective priors (see Ghosh, 2011).”
Penalising Model Component Complexity: A Principled, Practical Approach to Constructing Priors (2014, background): “” This condition can be made very precise, at the cost of being impossible to verify for complex models (Ghosal, Ghosh and van der Vaart, 2000, Theorem 2.4). The aim of this paper is to provide practical advice for setting priors, and so we commit the cardinal sin of mathematical sloppiness in an at”
Scale-Dependent Priors for Variance Parameters in Structured Additive Distributional Regression (2016, background): “Another branch of the literature encouraged the choice of ‘objective’ priors (Bernardo, 1979; Berger, 2006; Ghosh, 2011) or Jeffreys priors (Berger et al., 2009).”
A note on p-values interpreted as plausibilities (2012, background): “2011), Dempster–Shafer theory (Dempster 2008; Shafer 1976, 2011), generalized p-values and confidence intervals (Chiang 2001; Tsui and Weerahandi 1989; Weerahandi 1993), and Bayesian inference with default, reference, and/or data-dependent priors (Berger 2006; Berger et al. 2009; Fraser 2011; Fraser”