Related papers: Measuring Bayesian Robustness Using R\'enyi Diverg…
Robust Bayesian analysis has been mainly devoted to detecting and measuring robustness w.r.t. the prior distribution. Many contributions in the literature aim to define suitable classes of priors which allow the computation of variations of…
In Bayesian decision theory, it is known that robustness with respect to the loss and the prior can be improved by adding new observations. In this article we study the rate of robustness improvement with respect to the number of…
Bayesian simulation-based inference (SBI) methods are used in statistical models where simulation is feasible but the likelihood is intractable. Standard SBI methods can perform poorly in cases of model misspecification, and there has been…
In this paper we show that there is a link between approximate Bayesian methods and prior robustness. We show that what is typically recognized as an approximation to the likelihood, either due to the simulated data as in the Approximate…
Robust Bayesian linear regression is a classical but essential statistical tool. Although novel robustness properties of posterior distributions have been proved recently under a certain class of error distributions, their sufficient…
The standard approach to Bayesian inference is based on the assumption that the distribution of the data belongs to the chosen model class. However, even a small violation of this assumption can have a large impact on the outcome of a…
The practical implementation of Bayesian inference requires numerical approximation when closed-form expressions are not available. What types of accuracy (convergence) of the numerical approximations guarantee robustness and what types do…
In Bayesian analysis, the posterior follows from the data and a choice of a prior and a likelihood. One hopes that the posterior is robust to reasonable variation in the choice of prior, since this choice is made by the modeler and is often…
We introduce a methodology for robust Bayesian estimation with robust divergence (e.g., density power divergence or {\gamma}-divergence), indexed by a single tuning parameter. It is well known that the posterior density induced by robust…
This paper develops a methodology for robust Bayesian inference through the use of disparities. Metrics such as Hellinger distance and negative exponential disparity have a long history in robust estimation in frequentist inference. We…
This paper presents objective priors for robust Bayesian estimation against outliers based on divergences. The minimum $\gamma$-divergence estimator is well-known to work well estimation against heavy contamination. The robust Bayesian…
Robust Bayesian inference is the calculation of posterior probability bounds given perturbations in a probabilistic model. This paper focuses on perturbations that can be expressed locally in Bayesian networks through convex sets of…
Robustness checks are routine in empirical work, but there is no standard statistical procedure to formally measure what one can learn from them. I propose a "robustness radius" measure to quantify the amount by which the robustness checks…
Smoothing classifiers and probability density functions with Gaussian kernels appear unrelated, but in this work, they are unified for the problem of robust classification. The key building block is approximating the $\textit{energy…
In recent years, Bayesian inference in large-scale inverse problems found in science, engineering and machine learning has gained significant attention. This paper examines the robustness of the Bayesian approach by analyzing the stability…
We study the problem of robustly estimating the posterior distribution for the setting where observed data can be contaminated with potentially adversarial outliers. We propose Rob-ULA, a robust variant of the Unadjusted Langevin Algorithm…
Adversarial robustness of machine learning models is critical to ensuring reliable performance under data perturbations. Recent progress has been on point estimators, and this paper considers distributional predictors. First, using the link…
Bayesian inference and Gaussian processes are widely used in applications ranging from robotics and control to biological systems. Many of these applications are safety-critical and require a characterization of the uncertainty associated…
We introduce two kinds of risk measures with respect to some reference probability measure, which both allow for a certain order structure and domination property. Analyzing their relation to each other leads to the question when a certain…
Shape restrictions such as monotonicity on functions often arise naturally in statistical modeling. We consider a Bayesian approach to the problem of estimation of a monotone regression function and testing for monotonicity. We construct a…