Title: Robust Bayesian estimation by using the quasi-posterior with divergence
Authors: Tomoyuki Nakagawa - Tokyo University of Science (Japan) [presenting]
Abstract: In Bayesian analysis, it is well known that ordinary Bayesian estimators are not robust against outliers. Recently, robust Bayesian estimation against outliers has been proposed by using quasi-posterior and robust divergences. There are two type robust Bayesian estimators, one using the density power divergence and one using the $\gamma$-divergence. The robustness is characterized in term of the influence function. However, the calculation of the influence function is not easy. Furthermore, the estimator using the density power divergence does not work well for the estimation of the scale parameter, and it is unstable when the contamination ratio is not small. These properties are same from the frequentist viewpoint. On the other hand, from the frequentist viewpoint, it is well known that an estimator using the $\gamma$-divergence can make an estimation stable even when the contamination ratio is not small. Thus, we focus on the estimation using the gamma-divergence and compare the two type robust Bayesian estimations. We show the performance of this robust Bayes estimation in various situations.