Divergent Priors and well Behaved Bayes Factors

Arbeitspapier

Divergent priors are improper when defined on unbounded supports. Bartlett's paradox has been taken to imply that using improper priors results in ill-defined Bayes factors, preventing model comparison by posterior probabilities. However many improper priors have attractive properties that econometricians may wish to access and at the same time conduct model comparison. We present a method of computing well defined Bayes factors with divergent priors by setting rules on the rate of diffusion of prior certainty. The method is exact; no approximations are used. As a further result, we demonstrate that exceptions to Bartlett's paradox exist. That is, we show it is possible to construct improper priors that result in well defined Bayes factors. One important improper prior, the Shrinkage prior due to Stein (1956), is one such example. This example highlights pathologies with the resulting Bayes factors in such cases, and a simple solution is presented to this problem. A simple Monte Carlo experiment demonstrates the applicability of the approach developed in this paper.

Object Details

• Language: Englisch

References and Relationships

• Bibliographic citation: Series: Tinbergen Institute Discussion Paper ; No. 11-006/4

Classification and Topics

• Classification: Wirtschaft ; Bayesian Analysis: General ; Model Evaluation, Validation, and Selection ; Statistical Simulation Methods: General ; Multiple or Simultaneous Equation Models: Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
• Subject: Improper prior ; Bayes factor ; marginal likelihood ; Shrinkage prior ; Measure ; Bayes-Statistik ; Monte-Carlo-Methode ; Zeitreihenanalyse ; Theorie

Contributors, Places and Time

• Event: Geistige Schöpfung
• (who): Strachan, Rodney W. ; van Dijk, Herman K.
• Event: Veröffentlichung
• (who): Tinbergen Institute
• (where): Amsterdam and Rotterdam
• (when): 2011

Further information

• Handle: http://hdl.handle.net/10419/87023
• Last update: 10.03.2025, 11:43 AM CET