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Conditional Degree of Belief and Bayesian Inference

Published online by Cambridge University Press:  01 January 2022

Abstract

Why are conditional degrees of belief in an observation E, given a statistical hypothesis H, aligned with the objective probabilities expressed by H? After showing that standard replies (ratio analysis of conditional probability, chance-credence coordination) are not satisfactory, I develop a suppositional analysis of conditional degree of belief, transferring Ramsey’s classical proposal to statistical inference. The analysis saves the alignment, explains the role of chance-credence coordination, and rebuts the charge of arbitrary assessment of evidence in Bayesian inference. Finally, I explore the implications of this analysis for Bayesian reasoning with idealized models in science.

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Copyright © The Philosophy of Science Association

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Footnotes

I would like to thank Guido Bacciagaluppi, Max Bialek, Claus Beisbart, Colin Elliot, Alan Hájek, Stephan Hartmann, Jan-Willem Romeijn, Carlotta Pavese, Tom Sterkenburg, Olav Vassend, and audiences in Groningen, Sestri Levante, Tilburg, and Turin for their valuable feedback. Furthermore, three anonymous referees of Philosophy of Science contributed to improving this article. Research on this article was supported through the Starting Investigator grant 640638, “Making Scientific Inferences More Objective,” by the European Research Council.

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