Objective Bayesianism

I’m developing an account of objective Bayesianism. This is intended as a theory of rational degree of belief, rather than a theory of statistical inference.

The account is distinctive in that:

  • It rejects the usual Bayesian identification of conditional degree of belief with conditional probability.
  • It doesn’t presuppose that degrees of belief should be updated by Bayesian conditionalisation.
  • It rejects a common objective Bayesian supposition that evidence uniquely determines a rational belief function.
  • It takes objective chances to play a central role in determining rational degrees of belief.

The account is built on three kinds of norm:

  • Structural. An agent’s belief function should be a probability function.
  • Evidential. If the agent establishes from evidence that the chance function is in some set of probability functions, then her belief function should be in the convex hull of that set.
  • Equivocation. The agent’s degrees of belief should otherwise be equivocal, adopting committal degrees of belief (near 0 or 1) only where they are forced by structural or evidential norms.

Motivation

For some recent arguments for this sort of approach, see:

Jon Williamson: Bayesianism from a philosophical perspective and its application to medicine, International Journal of Biostatistics. doi: 10.1515/ijb-2022-0043

Jon Williamson: A Bayesian account of establishing, British Journal for the Philosophy of Science 73(4):903-925, 2022.. . doi: 10.1086/714798

Jon Williamson: Direct inference and probabilistic accounts of induction, Journal for General Philosophy of Science, 2022. . doi: 10.1007/s10838-021-09584-0

For an introduction to the approach, see:

Jon Williamson: In defence of objective Bayesianism, Oxford University Press, 2010.

Objective Bayesian inductive logic

I’m also interested in the use of objective Bayesianism to provide a new approach to inductive logic. I’m currently collaborating with Juergen Landes and Soroush Rafiee Rad on this.

Recent work includes:

Jon Williamson: Where do we stand on maximal entropy? In Logic for data, eds Hykel Hosni & Juergen Landes, Springer, 2024.

Juergen Landes, Soroush Rafiee Rad and Jon Williamson: Determining maximal entropy functions for objective Bayesian inductive logic, Journal of Philosophical Logic,  doi: 10.1007/s10992-022-09680-6

Juergen Landes, Soroush Rafiee Rad and Jon Williamson: Towards the Entropy-Limit Conjecture, Annals of Pure and Applied Logic 172(2):102870, 2021. . doi: 10.1016/j.apal.2020.102870

For an introduction to the approach, see:

Jon Williamson: Lectures on inductive logic, Oxford University Press, 2017. Errata.

Objective Bayesian nets

Graphical models can be used to represent and reason with objective Bayesian probabilities.

Recent work includes:

Juergen Landes and Jon Williamson: Objective Bayesian nets for integrating consistent datasets, Journal of Artificial Intelligence Research 74: 393-458, 2022. . doi 10.1613/jair.1.13363

For an introduction, see:

Rolf Haenni, Jan-Willem Romeijn, Gregory Wheeler & Jon Williamson: Probabilistic logics and probabilistic networks, Synthese Library, Springer, 2011.

Jon Williamson: Bayesian nets and causality: philosophical and computational foundations, Oxford University Press, 2005.