A1156
Title: Prediction for several infinitely divisible distribution models
Authors: Fumiyasu Komaki - The University of Tokyo (Japan) [presenting]
Abstract: In high-dimensional settings, predictive procedures based on shrinkage priors dominating noninformative priors such as the Jeffreys prior are effective in various models including normal, Poisson, and normal regression models. In the predictive theory of these models, the relationship between prediction and estimation based on the infinite divisibility of the underlying models and distributions plays an important role. The aim is to survey these results and discuss prediction problems for subordinators such as gamma distribution models, where shrinkage estimation remains meaningful even in one-dimensional settings. Additionally, how such exceptional behavior can be understood from the viewpoint of Bayesian prediction is discussed. In contrast to the normal and Poisson cases, estimation of Levy measures plays an essential role in these models.
