Iterative Markov Chain Monte Carlo Computation of Reference Priors and Minimax Risk
John Lafferty, Larry Wasserman
We present an iterative Markov chainMonte Carlo algorithm for computingreference priors and minimax risk forgeneral parametric families. Ourapproach uses MCMC techniques based onthe Blahut-Arimoto algorithm forcomputing channel capacity ininformation theory. We give astatistical analysis of the algorithm,bounding the number of samples requiredfor the stochastic algorithm to closelyapproximate the deterministic algorithmin each iteration. Simulations arepresented for several examples fromexponential families. Although we focuson applications to reference priors andminimax risk, the methods and analysiswe develop are applicable to a muchbroader class of optimization problemsand iterative algorithms.
PDF Link: /papers/01/p293-lafferty.pdf
AUTHOR = "John Lafferty
and Larry Wasserman",
TITLE = "Iterative Markov Chain Monte Carlo Computation of Reference Priors and Minimax Risk",
BOOKTITLE = "Proceedings of the Seventeenth Conference Annual Conference on Uncertainty in Artificial Intelligence (UAI-01)",
PUBLISHER = "Morgan Kaufmann",
ADDRESS = "San Francisco, CA",
YEAR = "2001",
PAGES = "293--300"