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

Herron, Timothy J.; Seidenfeld, Teddy; Wasserman, Larry

doi:10.1086/psaprocbienmeetp.1994.1.193030

Cited by 9 publications

(6 citation statements)

References 16 publications

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“…We see that dilation immune credible regions for the e-contaminated model have exactly the same form as regions from inverting a Jeffreys hypothesis test. For additional discussion of this idea, see $4 of Herron, Seidenfeld, and Wasserman 1994.…”

Section: And L Wassermanmentioning

confidence: 99%

Divisive Conditioning: Further Results on Dilation

1997

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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 dilationmanifests itself asymptotically in certain robust Bayesian models and we characterize the rate at which dilation occurs. 1. Introduction. An important part of the Bayesian statistical lore is that increasing shared evidence leads (almost surely) to merging opinions, provided those opinions are not extremely discrepant to begin with. This is one way to rebut charges of excessive subjectivism in Bayesian epistemology: use interpersonal agreement to show that objectivity results even though probability is "personal." In his classic discussion of Bayesian inference, Savage (1972, $3.6 and 4.6) illustrates "

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Section: And L Wassermanmentioning

confidence: 99%

Divisive Conditioning: Further Results on Dilation

1997

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“…It is clear that precise credal states are dilation-immune since inf{P (H|E)} = sup{P (H|E)} for all H and E in F such that P (H|E) is defined. Consider the following common example of dilation, introduced in outline earlier (Herron et al, 1994;Pedersen and Wheeler, 2015). We simplify by assuming that P consists of just two probabilities.…”

Section: Dilationmentioning

confidence: 99%

“…There is by now a fairly extensive literature on dilation (e.g.,Walley, 1991;Seidenfeld and Wasserman, 1993;Herron et al, 1994;Wasserman and Seidenfeld, 1994;Herron et al, 1997;Bradley and Steele, 2014; Wheeler, 2014, 2015;Nielsen and Stewart, 2019;Moss, 2020).…”

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Distention for Sets of Probabilities

Stewart¹,

Nielsen

2022

Philos. sci.

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Bayesians often appeal to “merging of opinions” to rebut charges of excessive subjectivity. But what happens in the short run is often of greater interest than what happens in the limit. Seidenfeld and coauthors use this observation as motivation for investigating the counterintuitive short run phenomenon of dilation since, they allege, dilation is “the opposite” of asymptotic merging of opinions. The measure of uncertainty relevant for dilation, however, is not the one relevant for merging of opinions. We investigate the short run behavior of the metric relevant for merging, and show that dilation is independent of the opposite of merging.

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“…We offer another, more extreme example of polarization adapted from (Herron et al, 1994;Pedersen and Wheeler, 2015).…”

Section: Polarizationmentioning

confidence: 99%

“…The mathematics of dilation has been extensively studied in a series of articles (Seidenfeld and Wasserman, 1993;Herron et al, 1994;Wasserman and Seidenfeld, 1994;Herron et al, 1997;Wheeler, 2014, 2015). For results related to our Theorem 1, see in particular Wasserman and Seidenfeld's Result 1 (1994), and Pedersen and Wheeler's Theorem 1 and its corollary (2015).…”

Section: Dilationmentioning

confidence: 99%

Persistent Disagreement and Polarization in a Bayesian Setting

Nielsen¹,

Stewart²

2021

The British Journal for the Philosophy of Science

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For two ideally rational agents, does learning a finite amount of shared evidence necessitate agreement? No. But does it at least guard against belief polarization, the case in which their opinions get further apart? No. OK, but are rational agents guaranteed to avoid polarization if they have access to an infinite, increasing stream of shared evidence? No. 1Introduction2The Finite Case 2.1Polarization2.2Dilation2.3Global polarization3The General Case 3.1Merging of opinions3.2The Bayesian consensus-or-polarization law4DiscussionAppendix

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

Cited by 9 publications

References 16 publications

Divisive Conditioning: Further Results on Dilation

Divisive Conditioning: Further Results on Dilation

Distention for Sets of Probabilities

Persistent Disagreement and Polarization in a Bayesian Setting

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