On Priors With a Kullback–Leibler Property

Stephen Walker Stephen Walker is Professor, Department of Mathematics, University of Bath, Bath, England. Paul Damien is The B. M. Rankin Jr., Professor of Business Administration, Professor of Management Science and Information Systems, and Professor of Finance, McCombs School of Business, University of Texas as Austin, Austin, TX 78712, USA. Peter Lenk is Associate Professor, Michigan Business School, Ann Arbor, MI 48109, USA. The work of S. Walker is financially supported by an EPSRC Advanced Research Fellowship. The authors are grateful for the detailed comments of two referees and an associate editor.

Paul Damien Stephen Walker is Professor, Department of Mathematics, University of Bath, Bath, England. Paul Damien is The B. M. Rankin Jr., Professor of Business Administration, Professor of Management Science and Information Systems, and Professor of Finance, McCombs School of Business, University of Texas as Austin, Austin, TX 78712, USA. Peter Lenk is Associate Professor, Michigan Business School, Ann Arbor, MI 48109, USA. The work of S. Walker is financially supported by an EPSRC Advanced Research Fellowship. The authors are grateful for the detailed comments of two referees and an associate editor.

Peter Lenk Stephen Walker is Professor, Department of Mathematics, University of Bath, Bath, England. Paul Damien is The B. M. Rankin Jr., Professor of Business Administration, Professor of Management Science and Information Systems, and Professor of Finance, McCombs School of Business, University of Texas as Austin, Austin, TX 78712, USA. Peter Lenk is Associate Professor, Michigan Business School, Ann Arbor, MI 48109, USA. The work of S. Walker is financially supported by an EPSRC Advanced Research Fellowship. The authors are grateful for the detailed comments of two referees and an associate editor.

Abstract

In this paper, we highlight properties of Bayesian models in which the prior puts positive mass on all Kullback–Leibler neighborhoods of all densities. These properties are concerned with model choice via the Bayes factor, density estimation and the maximization of expected utility for decision problems. In four illustrations we focus on the Bayes factor and show that whatever models are being compared, the [log(Bayes factor)]/[sample size] converges to a non-random number which has a nice interpretation. A parametric versus semiparametric model comparison provides a fifth illustration.

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On Priors With a Kullback–Leibler Property

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On Priors With a Kullback–Leibler Property

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