Arbeitspapier
Divergent Priors and well Behaved Bayes Factors
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.
- Sprache
-
Englisch
- Erschienen in
-
Series: Tinbergen Institute Discussion Paper ; No. 11-006/4
- Klassifikation
-
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
- Thema
-
Improper prior
Bayes factor
marginal likelihood
Shrinkage prior
Measure
Bayes-Statistik
Monte-Carlo-Methode
Zeitreihenanalyse
Theorie
- Ereignis
-
Geistige Schöpfung
- (wer)
-
Strachan, Rodney W.
van Dijk, Herman K.
- Ereignis
-
Veröffentlichung
- (wer)
-
Tinbergen Institute
- (wo)
-
Amsterdam and Rotterdam
- (wann)
-
2011
- Handle
- Letzte Aktualisierung
-
10.03.2025, 11:43 MEZ
Datenpartner
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Objekttyp
- Arbeitspapier
Beteiligte
- Strachan, Rodney W.
- van Dijk, Herman K.
- Tinbergen Institute
Entstanden
- 2011
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