“What ever happened to Bayesian foundations?” was one of the final topics of our seminar (Mayo/SpanosPhil6334). In the past 15 years or so, not only have (some? most?) Bayesians come to accept violations of the Likelihood Principle, they have also tended to disown Dutch Book arguments, and the very idea of inductive inference as updating beliefs by Bayesian conditionalization has evanescencd. In one of Thursday’s readings, by Baccus, Kyburg, and Thalos (1990), it is argued that under certain conditions, it is never a rational course of action to change belief by Bayesian conditionalization. Here’s a short snippet for your Saturday night reading (the full paper is https://errorstatistics.files.wordpress.com/2014/05/bacchus_kyburg_thalos-against-conditionalization.pdf): Continue reading
Posts Tagged With: Kyburg
(1) If discretionary judgments are thought to introduce subjectivity in inference, a classic strategy thought to achieve objectivity is to extricate such choices, replacing them with purely formal a priori computations or agreed-upon conventions (see March 14). If leeway for discretion introduces subjectivity, then cutting off discretion must yield objectivity! Or so some argue. Such strategies may be found, to varying degrees, across the different approaches to statistical inference.
The inductive logics of the type developed by Carnap promised to be an objective guide for measuring degrees of confirmation in hypotheses, despite much-discussed problems, paradoxes, and conflicting choices of confirmation logics. In Carnapian inductive logics, initial assignments of probability are based on a choice of language and on intuitive, logical principles. The consequent logical probabilities can then be updated (given the statements of evidence) with Bayes’s Theorem. The fact that the resulting degrees of confirmation are at the same time analytical and a priori—giving them an air of objectivity–reveals the central weakness of such confirmation theories as “guides for life”, e.g., —as guides, say, for empirical frequencies or for finding things out in the real world. Something very similar happens with the varieties of “objective’” Bayesian accounts, both in statistics and in formal Bayesian epistemology in philosophy (a topic to which I will return; if interested, see my RMM contribution).
A related way of trying to remove latitude for discretion might be to define objectivity in terms of the consensus of a specified group, perhaps of experts, or of agents with “diverse” backgrounds. Once again, such a convention may enable agreement yet fail to have the desired link-up with the real world. It would be necessary to show why consensus reached by the particular choice of group (another area for discretion) achieves the learning goals of interest.