# Objective Bayesianism

My account of objective Bayesianism is epistemological: 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 assumption 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.

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**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 *19(2): 295-307, 2023. 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* 54:451–472, 2023. . 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.

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**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* 52:555-608, 2023. 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.

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**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.