Nonstandard Bayesianism: How Verisimilitude and Counterfactual Degrees of Belief Solve the Interpretive Problem in Bayesian Inference

Scientists and Bayesian statisticians often study hypotheses that they know to be false. This creates an interpretive problem because the Bayesian probability of a hypothesis is typically interpreted as a degree of belief that the hypothesis is true. In this paper, I present and contrast two solutions to the interpretive problem, both of which involve reinterpreting the Bayesian framework in such a way that pragmatic factors directly determine in part how probability assignments are interpreted and whether a given probability assignment is rational. I argue that there is an important sense in which the two solutions are equivalent, and I suggest that the two reinterpretations can help us do Bayesian inference better. I also explore various features of the two reinterprations, including their relations to the standard Bayesian interpretation of probability and to the Law of Likelihood

Nonstandard Bayesianism: How Verisimilitude and Counterfactual Degrees of Belief Solve the Interpretive Problem in Bayesian Inference

Scientists and Bayesian statisticians often study hypotheses that they know to be false. This creates an interpretive problem because the Bayesian probability of a hypothesis is typically interpreted as a degree of belief that the hypothesis is true. In this paper, I present and contrast two solutions to the interpretive problem, both of which involve reinterpreting the Bayesian framework in such a way that pragmatic factors directly determine in part how probability assignments are interpreted and whether a given probability assignment is rational. I argue that there is an important sense in which the two solutions are equivalent, and I suggest that the two reinterpretations can help us do Bayesian inference better. I also explore various features of the two reinterprations, including their relations to the standard Bayesian interpretation of probability and to the Law of Likelihood

Bayesian Statistical Inference and Approximate Truth

Scientists and Bayesian statisticians often study hypotheses that they know to be false. This creates an interpretive problem because the Bayesian probability of a hypothesis is supposed to represent the probability that the hypothesis is true. I investigate whether Bayesianism can accommodate the idea that false hypotheses are sometimes approximately true or that some hypotheses or models can be closer to the truth than others. I argue that the idea that some hypotheses are approximately true in an absolute sense is hard to square with Bayesianism, but that the notion that some hypotheses are comparatively closer to the truth than others can be made compatible with Bayesianism, and that this provides an adequate and potentially useful solution to the interpretive problem. Finally, I compare my ``verisimilitude'' solution to the interpretive problem with a ``counterfactual'' solution recently proposed by Jan Sprenger

Bayesian Statistical Inference and Approximate Truth

Scientists and Bayesian statisticians often study hypotheses that they know to be false. This creates an interpretive problem because the Bayesian probability of a hypothesis is supposed to represent the probability that the hypothesis is true. I investigate whether Bayesianism can accommodate the idea that false hypotheses are sometimes approximately true or that some hypotheses or models can be closer to the truth than others. I argue that the idea that some hypotheses are approximately true in an absolute sense is hard to square with Bayesianism, but that the notion that some hypotheses are comparatively closer to the truth than others can be made compatible with Bayesianism, and that this provides an adequate and potentially useful solution to the interpretive problem. Finally, I compare my ``verisimilitude'' solution to the interpretive problem with a ``counterfactual'' solution recently proposed by Jan Sprenger

Confirmation Measures and Sensitivity

Stevens (1946) draws a useful distinction between ordinal scales, interval scales, and ratio scales. Most recent discussions of confirmation measures have proceeded on the ordinal level of analysis. In this paper, I give a more quantitative analysis. In particular, I show that the requirement that our desired confirmation measure be at least an \emph{interval} measure naturally yields necessary conditions that jointly entail the log-likelihood measure. Thus I conclude that the log-likelihood measure is the only good candidate interval measure

A verisimilitude framework for inductive inference, with an application to phylogenetics

Bayesianism and likelihoodism are two of the most important frameworks philosophers of science use to analyse scientific methodology. However, both frameworks face a serious objection: much scientific inquiry takes place in highly idealized frameworks where all the hypotheses are known to be false. Yet, both Bayesianism and likelihoodism seem to be based on the assumption that the goal of scientific inquiry is always truth rather than closeness to the truth. Here, I argue in favour of a verisimilitude framework for inductive inference. In the verisimilitude framework, scientific inquiry is conceived of, in part, as a process where inference methods ought to be calibrated to appropriate measures of closeness to the truth. To illustrate the verisimilitude framework, I offer a reconstruction of parsimony evaluations of scientific theories, and I give a reconstruction and extended analysis of the use of parsimony inference in phylogenetics. By recasting phylogenetic inference in the verisimilitude framework, it becomes possible to both raise and address objections to phylogenetic methods that rely on parsimony.Nanyang Technological UniversityPublished versionResearch for this article was supported by Nanyang Technological University Start-Up Grant (no. M4082134)