Title: Robust Bayesian estimation using the gamma divergence
Authors: Tomoyuki Nakagawa - Tokyo University of Science (Japan) [presenting]
Shintaro Hashimoto - Hiroshima University (Japan)
Abstract: In the Bayesian analysis, it is well known that ordinary Bayesian estimator is not robust against outliers. The robust Bayesian estimation against outliers is proposed by using the density power divergence. They characterized the robustness in terms of the influence function. However, it is known that the estimator using the density power divergence does not work well the estimation for the scale parameter, and are unstable when the contamination ratio is not small. These facts were discussed previously in a frequentist viewpoint. However, it was shown that the estimator using the gamma divergence can make a stable estimate even when the contamination ratio is not small. We propose the robust Bayesian estimation using the gamma divergence. Furthermore, the selection of priors is also an important problem in the robust Bayesian estimation. We also propose the two type objective priors for the robust Bayesian estimation.