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