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A Further Look at the Bayes Blind Spot

Shattuck, Mark and Wagner, Carl (2022) A Further Look at the Bayes Blind Spot. [Preprint]


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Abstract. Gyenis and R ́edei have demonstrated that any prior p on a finite algebra, however chosen, severely restricts the set of posteriors accessible from p by Jeffrey conditioning on a nontrivial partition. Their demonstration involves showing that the set of posteriors not accessible from p in this way (which they call the Bayes blind spot of p) is large with respect to three common measures of size, namely, having cardinality c, (normalized) Lebesgue measure 1, and Baire second category with respect to a natural topology. In the present paper, we establish analogous results for probability measures defined on any infinite sigma algebra of subsets of a denumerably infinite set. However, we have needed to employ distinctly dfferent approaches to determine the cardinality, and especially, the topological and measure- theoretic sizes of the Bayes blind spot in the infinite case. Interestingly, all of the results that we establish for a single prior p continue to hold for the intersection of the Bayes blind spots of countably many priors. This leads us to conjecture that Bayesian learning itself might be just as culpable as the limitations imposed by priors in enabling the existence of large Bayes blind spots.

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Item Type: Preprint
Keywords: Bayes blind spot, Jeffrey conditioning, Baire category, Bayesian learning
Subjects: Specific Sciences > Probability/Statistics
Depositing User: Dr. Carl Wagner
Date Deposited: 08 Jun 2022 02:29
Last Modified: 08 Jun 2022 02:29
Item ID: 20719
Subjects: Specific Sciences > Probability/Statistics
Date: 5 June 2022

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