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arXiv · 1311.1067

Approximation of improper priors

Christele Bioche·Pierre Druilhet
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Abstract

We propose a convergence mode for positive Radon measures which allows a sequence of probability measures to have an improper limiting measure. We define a sequence of vague priors as a sequence of probability measures that converges to an improper prior. We consider some cases where vague priors have necessarily large variances and other cases where they have not. We study the consequences of the convergence of prior distributions on the posterior analysis. Then we give some constructions of vague priors that approximate the Haar measures or the Jeffreys priors. We also revisit the Jeffreys-Lindley paradox.

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Christele Bioche, Pierre Druilhet. 2016-03-30. Approximation of improper priors. https://doi.org/10.3150/15-bej708

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