Robust Bayesian estimation via the K-divergence

In this paper, we introduce a novel framework for robust Bayesian parameter estimation using the K-divergence. The framework incorporates an outlier resilient pseudo-posterior density function, called the K-posterior, which is based on an empirical version of the K-divergence. The latter involves utilizing Parzen's non-parametric Kernel density estimator to mitigate the influence of outliers. Under the quadratic loss, a new robust analog of the posterior mean estimator (PME), referred here to as the KPME, is obtained. In the paper, we examine the asymptotic behavior of the KPME and investigate its robustness in the presence of outliers. Furthermore, we tackle the task of data-guided selection for the bandwidth parameter of the kernel in order to optimize a performance-oriented objective. Lastly, the KPME is successfully applied to robust Bayesian source localization under intermittent jamming.