Robust approximate Bayesian inference

Approximate Decentralized Bayesian Inference

This paper presents an approximate method for performing Bayesian inference in models with conditional independence over a decentralized network of learning agents. The method first employs variational inference on each individual learning agent to generate a local approximate posterior, the agents transmit their local posteriors to other agents in the network, and finally each agent combines i...

Approximate Bayesian Inference for Quantiles

Suppose data consist of a random sample from a distribution function FY , which is unknown, and that interest focuses on inferences on θ, a vector of quantiles of FY . When the likelihood function is not fully specified, a posterior density cannot be calculated and Bayesian inference is difficult. This article considers an approach which relies on a substitution likelihood characterized by a ve...

Robust Sequential Approximate Bayesian Estimation

An approximation tothe sequential updating of the distribution flocation parameters of a linear time series model is developed for non-normal observations. The behaviour of the resulting non-linear recursive filtering algorithm isexamined and shown to have certain desirable properties for a variety of non-normal error distributions. Illustrative examples are given and relationships with previou...

Robust and Private Bayesian Inference

We examine the robustness and privacy of Bayesian inference, under assumptions on the prior, and with no modifications to the Bayesian framework. First, we generalise the concept of differential privacy to arbitrary dataset distances, outcome spaces and distribution families. We then prove bounds on the robustness of the posterior, introduce a posterior sampling mechanism, show that it is diffe...

Approximate Inference in Structured Bayesian Networks