In this paper, we introduce a novel framework for robust Bayesian parameter estimation using the -divergence. The framework incorporates an outlier resilient pseudo-posterior density function, called the -posterior, which is based on an empirical version of the -divergence. The latter involves utilizing Parzen’s non-parametric ernel 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 PME, is obtained. In the paper, we examine the asymptotic behavior of the PME 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 PME is successfully applied to robust Bayesian source localization under intermittent jamming.

中文翻译：

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通过[公式省略]-散度进行稳健贝叶斯估计

在本文中，我们介绍了一种使用 散度进行鲁棒贝叶斯参数估计的新颖框架。该框架包含了一个离群弹性伪后验密度函数，称为 -后验，它基于 -散度的经验版本。后者涉及利用 Parzen 的非参数核密度估计器来减轻异常值的影响。在二次损失下，获得了后验均值估计器（PME）的新的鲁棒模拟，这里称为PME。在本文中，我们研究了 PME 的渐近行为，并研究了其在存在异常值的情况下的鲁棒性。此外，我们还解决了内核带宽参数的数据引导选择任务，以优化面向性能的目标。最后，PME 成功应用于间歇性干扰下的鲁棒贝叶斯源定位。