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Divisive Conditioning: Further Results on Dilation

Published online by Cambridge University Press:  01 April 2022

Timothy Herron ,
Teddy Seidenfeld  and
Larry Wasserman
Timothy Herron*
Affiliation:
Department of Philosophy, Carnegie Mellon University
Teddy Seidenfeld*
Affiliation:
Departments of Philosophy and Statistics, Carnegie Mellon University
Larry Wasserman*
Affiliation:
Department of Statistics, Carnegie Mellon University
*
†Send reprint requests to the second or third author, Department of Statistics, Carnegie Mellon University, 5000 Forbes Avenue, Pittsburgh, PA 15213-3890.
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Abstract

Conditioning can make imprecise probabilities uniformly more imprecise. We call this effect “dilation”. In a previous paper (1993), Seidenfeld and Wasserman established some basic results about dilation. In this paper we further investigate dilation on several models. In particular, we consider conditions under which dilation persists under marginalization and we quantify the degree of dilation. We also show that dilation manifests itself asymptotically in certain robust Bayesian models and we characterize the rate at which dilation occurs.

Type
Research Article
Information
Philosophy of Science , Volume 64 , Issue 3 , September 1997 , pp. 411 - 444
Copyright
Copyright © Philosophy of Science Association 1997

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Footnotes

‡

The first two authors were supported by NSF Grant SES-9208942. The third author was supported by NSF Grants DMS-9005858 and DMS-9357646 and NIH Grant RO1-CA54852-01.

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