B0992
Title: Iterative algorithms for constructing priors
Authors: Fumiyasu Komaki - RIKEN CBS (Japan) [presenting]
Abstract: Two iterative algorithms to construct prior densities for Bayesian prediction based on parametric models are discussed. First, an algorithm to construct latent information priors is introduced. The latent information prior is defined as a prior maximizing the conditional mutual information between the quantity to be predicted and the unknown parameter given the data. Bayesian predictive densities based on the latent information priors achieve minimaxity under the Kullback-Leibler loss in many examples. The algorithm is a generalization of the Arimoto-Blahut algorithm to obtain channel capacity in information theory. Next, an algorithm to obtain Bayes projection of a non-Bayesian predictive density is introduced. The Bayes projection is defined as a divergence projection of a predictive density to the space of Bayesian predictive densities. The Bayes projection of a predictive density is superior to the original predictive density under the Kullback-Leibler loss. The two introduced algorithms are closely related to each other.
