2008-07-09-grunwald08a.md

title	abstract	layout	series	publisher	issn	id	month	tex_title	firstpage	lastpage	page	order	cycles	bibtex_editor	editor	bibtex_author	author	date	note	address	container-title	volume	genre	issued	pdf	extras
A game-theoretic analysis of updating sets of probabilities	We consider how an agent should update her uncertainty when it is represented by a set P of probability distributions and the agent observes that a random variable X takes on value x, given that the agent makes decisions using the minimax criterion, perhaps the best-studied and most commonly-used criterion in the literature. We adopt a game-theoretic framework, where the agent plays against a bookie, who chooses some distribution from P. We consider two reasonable games that differ in what the bookie knows when he makes his choice. Anomalies that have been observed before, like time inconsistency, can be understood as arising because different games are being played, against bookies with different information. We characterize the important special cases in which the optimal decision rules according to the minimax criterion amount to either conditioning or simply ignoring the information. Finally, we consider the relationship between conditioning and calibration when uncertainty is described by sets of probabilities.	inproceedings	Proceedings of Machine Learning Research	PMLR	2640-3498	grunwald08a	0	A game-theoretic analysis of updating sets of probabilities	240	247	240-247	240	false	McAllester, David A. and Myllym{"a}ki, Petri	given family David A. McAllester given family Petri Myllymäki	Gr\"{u}nwald, Peter D. and Halpern, Joseph Y.	given family Peter D. Grünwald given family Joseph Y. Halpern	2008-07-09	Reissued by PMLR on 30 October 2024.		Proceedings of the 24th Conference on Uncertainty in Artificial Intelligence	R6	inproceedings	date-parts 2008 7 9	http://proceedings.mlr.press/r6/grunwald08a/grunwald08a.pdf