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New Semantics for Bayesian Inference: The Interpretive Problem and Its Solutions

Vassend, Olav Benjamin (2018) New Semantics for Bayesian Inference: The Interpretive Problem and Its Solutions. [Preprint]

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Abstract

Scientists and Bayesian statisticians often study hypotheses that they know to be false. This creates an interpretive problem because the Bayesian probability assigned to a hypothesis is typically interpreted as the probability that the hypothesis is true. I argue that solving the interpretive problem requires coming up with a new semantics for Bayesian inference. I present and contrast two solutions to the interpretive problem, both of which involve giving a new interpretation of probability. I argue that both of these new interpretations of Bayesian inference have the same advantages that the standard interpretation has, but that they have the added benefit of being applicable in a wider set of circumstances. I furthermore show that the two new interpretations are inter-translatable and I explore the conditions under which they are co-extensive with the standard Bayesian interpretation. Finally, I argue that the solutions to the interpretive problem support the claim that there is pervasive pragmatic encroachment on whether a given Bayesian probability assignment is rational.


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Item Type: Preprint
Creators:
CreatorsEmailORCID
Vassend, Olav Benjaminvassend@ntu.edu.sg
Keywords: Bayesian inference, idealized models, statistical inference, Bayesian semantics
Subjects: General Issues > Models and Idealization
Specific Sciences > Probability/Statistics
Depositing User: Olav Vassend
Date Deposited: 29 Oct 2018 19:56
Last Modified: 29 Oct 2018 19:56
Item ID: 15215
Subjects: General Issues > Models and Idealization
Specific Sciences > Probability/Statistics
Date: 27 October 2018
URI: https://philsci-archive-dev.library.pitt.edu/id/eprint/15215

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