The Extent of Dilation of Sets of Probabilities and the Asymptotics of Robust Bayesian Inference

We report two issues concerning diverging sets of Bayesian (conditional) probabilities-divergence of "posteriors"-that can result with increasing evidence. Consider a set P of probabilities typically, but not always, based on a set of Bayesian "priors." Fix E, an event of interest, and X, a random variable to be observed. With respect to P, when the set of conditional probabilities for E, given X, strictly contains the set of unconditional probabilities for E, for each possible outcome X = x, call this phenomenon dilation of the set of probabilities (Seidenfeld and Wasserman 1993). Thus, dilation contrasts with the asymptotic merging of posterior probabilities reported by Savage (1954) and by Blackwell and Dubins (1962). (1) In a wide variety of models for Robust Bayesian inference the extent to which X dilates E is related to a model specific index of how far key elements of P are from a distribution that makes X and E independent. (2) At a fixed confidence level, (1-α), Classical interval estimates A n for, e.g., a Normal mean θ have length O(n -1/2 ) (for sample size n). Of course, the confidence level correctly reports the (prior) probability that θ ∈ A n ,P(A n )=1-α , independent of the prior for θ . However, as shown by Pericchi and Walley (1991), if an ε -contamination class is used for the prior on the parameter θ , there is asymptotic (posterior) dilation for the A n , given the data. If, however, the intervals A ′ n are chosen with length $O(\sqrt{\log (\text{n})/\text{n})}$ , then there is no asymptotic dilation. We discuss the asymptotic rates of dilation for ClassClassical and Bayesian interval estimates and relate these to Bayesian hypothesis testing.
Keywords No keywords specified (fix it)
Categories (categorize this paper)
 Save to my reading list
Follow the author(s)
My bibliography
Export citation
Find it on Scholar
Edit this record
Mark as duplicate
Revision history
Request removal from index
Download options
Our Archive

Upload a copy of this paper     Check publisher's policy     Papers currently archived: 26,692
External links

Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library
References found in this work BETA

No references found.

Add more references

Citations of this work BETA
Demystifying Dilation.Arthur Paul Pedersen & Gregory Wheeler - 2014 - Erkenntnis 79 (6):1305-1342.
Belief and Contextual Acceptance.Eleonora Cresto - 2010 - Synthese 177 (1):41-66.

Add more citations

Similar books and articles
Optimum Inductive Methods.R. Festa - 1993 - Kluwer Academic Publishers: Dordrecht.
Constraining Prior Probabilities of Phylogenetic Trees.Bengt Autzen - 2011 - Biology and Philosophy 26 (4):567-581.
Defeasible Conditionalization.Paul D. Thorn - 2014 - Journal of Philosophical Logic 43 (2-3):283-302.
On the Nature of Bayesian Convergence.James Hawthorne - 1994 - PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1994:241 - 249.
Getting Fancy with Probability.Henry E. Kyburg - 1992 - Synthese 90 (2):189-203.
Getting Fancy with Probability.Henry E. Kyburg Jr - 1992 - Synthese 90 (2):189 - 203.
The Prior Probabilities of Phylogenetic Trees.Joel D. Velasco - 2008 - Biology and Philosophy 23 (4):455-473.
Conditional Probabilities.A. R. Pruss - 2012 - Analysis 72 (3):488-491.

Monthly downloads

Added to index


Total downloads

10 ( #427,259 of 2,158,398 )

Recent downloads (6 months)

2 ( #194,528 of 2,158,398 )

How can I increase my downloads?

My notes
Sign in to use this feature

There  are no threads in this forum
Nothing in this forum yet.

Other forums