B0328
Title: Improved prediction for independent Poisson processes under Kullback-Leibler loss
Authors: Xiao Li - The University of Tokyo (Japan) [presenting]
Fumiyasu Komaki - RIKEN CBS (Japan)
Abstract: Simultaneous predictive distributions are considered for independent Poisson observables and the performance of predictive distributions is evaluated using the Kullback--Leibler loss. It is shown that Bayesian predictive distributions based on priors constructed using superharmonic functions dominate the Bayesian predictive distribution based on the Jeffreys prior. The K-L risk of the improved predictions is demonstrated to be less than 1.04 times a minimax lower bound. On the basis of the result, a class of priors is proposed called mix subspace shrinkage prior. Their effectiveness is demonstrated in experiments with both simulated data and real data.
