743

**Iterative Markov Chain Monte Carlo Computation of Reference
Priors and Minimax Risk**

**John Lafferty and Larry Wasserman**

### Abstract:

We present an iterative Markov chain Monte Carlo algorithm for
computing reference priors and minimax risk for general parametric
families. Our approach uses MCMC techniques based on the
Blahut-Arimoto algorithm for computing channel capacity in information
theory. We give a statistical analysis of the algorithm, bounding the
numbers of samples required for ties to chaotic algorithm to closely
approximate the deterministic algorithm in each iteration. Simulations
are presented for several examples from exponential families. Although
we focus on applications to reference priors and minimax risk, the
methods and analysis we develop are applicable to a much broader class
of optimization problems and iterative algorithms.

*Heidi Sestrich*

*7/23/2001*
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