Bayesian Decision Theory and Stochastic Independence

Philosophy of Science (forthcoming)

Authors
Philippe Mongin
Centre National de la Recherche Scientifique
Abstract
Stochastic independence (SI) has a complex status in probability theory. It is not part of the definition of a probability measure, but it is nonetheless an essential property for the mathematical development of this theory, hence a property that any theory on the foundations of probability should be able to account for. Bayesian decision theory, which is one such theory, appears to be wanting in this respect. In Savage's classic treatment, postulates on preferences under uncertainty are shown to entail a subjective expected utility (SEU) representation, and this permits asserting only the existence and uniqueness of a subjective probability, regardless of its properties. What is missing is a preference postulate that would specifically connect with the SI property. The paper develops a version of Bayesian decision theory that fills this gap. In a framework of multiple sources of uncertainty, we introduce preference conditions that jointly entail the SEU representation and the property that the subjective probability in this representation treats the sources of uncertainty as being stochastically independent. We give two representation theorems of graded complexity to demonstrate the power of our preference conditions. Two sections of comments follow, one connecting the theorems with earlier results in Bayesian decision theory, and the other connecting them with the foundational discussion on SI in probability theory and the philosophy of probability. Appendices offer more technical material.
Keywords Probability theory  Stochastic independence  Probabilistic independence  Subjective probability  Subjective expected utility  Bayesian decision theory  Preference axiomatization  Representation theorems  Separability theory  Savage
Categories (categorize this paper)
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

Our Archive
External links

Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library

References found in this work BETA

A Nonpragmatic Vindication of Probabilism.James Joyce - 1998 - Philosophy of Science 65 (4):575-603.
Decision Theory with a Human Face.Richard Bradley - 2017 - Cambridge University Press.
The Foundations of Causal Decision Theory.Isaac Levi & James M. Joyce - 1999 - Journal of Philosophy 97 (7):387.
Philosophical Theories of Probability.Donald Gillies - 2003 - Philosophical Quarterly 53 (210):132-134.

View all 11 references / Add more references

Citations of this work BETA

Add more citations

Similar books and articles

Bayesian Probability.Patrick Maher - 2010 - Synthese 172 (1):119 - 127.
Risk and Tradeoffs.Lara Buchak - 2014 - Erkenntnis 79 (S6):1091-1117.
A Foundation of Bayesian Statistics.R. Kast - 1991 - Theory and Decision 31 (2-3):175-197.
Probability, Objectivity, and Induction.Arnold Baise - 2013 - Journal of Ayn Rand Studies 13 (2):81-95.
An Introduction to Decision Theory.Martin Peterson - 2009 - Cambridge University Press.
Decision Theory.Lara Buchak - 2016 - In Christopher Hitchcock & Alan Hajek (eds.), Oxford Handbook of Probability and Philosophy. Oxford University Press.
A Unified Bayesian Decision Theory.Richard Bradley - 2007 - Theory and Decision 63 (3):233-263,.
A Rule For Updating Ambiguous Beliefs.Cesaltina Pacheco Pires - 2002 - Theory and Decision 53 (2):137-152.

Analytics

Added to PP index
2019-04-18

Total views
46 ( #173,144 of 2,250,068 )

Recent downloads (6 months)
46 ( #14,856 of 2,250,068 )

How can I increase my downloads?

Downloads

My notes

Sign in to use this feature