Related papers: Likelihood distortion and Bayesian local robustnes…

In the presence of model risk, it is well-established to replace classical expected values by worst-case expectations over all models within a fixed radius from a given reference model. This is the "robustness" approach. We show that…

Likelihood-based inferences have been remarkably successful in wide-spanning application areas. However, even after due diligence in selecting a good model for the data at hand, there is inevitably some amount of model misspecification:…

Selection bias arises when the probability that an observation enters a dataset depends on variables related to the quantities of interest, leading to systematic distortions in estimation and uncertainty quantification. For example, in…

For a Bayesian, the task to define the likelihood can be as perplexing as the task to define the prior. We focus on situations when the parameter of interest has been emancipated from the likelihood and is linked to data directly through a…

Datasets are rarely a realistic approximation of the target population. Say, prevalence is misrepresented, image quality is above clinical standards, etc. This mismatch is known as sampling bias. Sampling biases are a major hindrance for…

The most popular hypothesis testing procedure, the likelihood ratio test, is known to be highly non-robust in many real situations. Basu et al. (2013a) provided an alternative robust procedure of hypothesis testing based on the density…

Outliers can seriously distort statistical inference by inducing excessive sensitivity in the likelihood function, thereby compromising the reliability of Bayesian estimation. To address this issue, we develop a robust Bayesian estimation…

We propose a robust Bayesian formulation of random feature (RF) regression that accounts explicitly for prior and likelihood misspecification via Huber-style contamination sets. Starting from the classical equivalence between…

We propose a general method to carry out a valid Bayesian analysis of a finite-dimensional `targeted' parameter in the presence of a finite-dimensional nuisance parameter. We apply our methods to causal inference based on estimating…

In a reinforcement learning (RL) setting, the agent's optimal strategy heavily depends on her risk preferences and the underlying model dynamics of the training environment. These two aspects influence the agent's ability to make…

Bayesian statistics is concerned with conducting posterior inference for the unknown quantities in a given statistical model. Conventional Bayesian inference requires the specification of a probabilistic model for the observed data, and the…

Bayesian estimation is increasingly popular for performing model based inference to support policymaking. These data are often collected from surveys under informative sampling designs where subject inclusion probabilities are designed to…

This paper proposes an online, provably robust, and scalable Bayesian approach for changepoint detection. The resulting algorithm has key advantages over previous work: it provides provable robustness by leveraging the generalised Bayesian…

Modern machine learning applications should be able to address the intrinsic challenges arising over inference on massive real-world datasets, including scalability and robustness to outliers. Despite the multiple benefits of Bayesian…

Models with intractable likelihood functions arise in areas including network analysis and spatial statistics, especially those involving Gibbs random fields. Posterior parameter es timation in these settings is termed a doubly-intractable…

Some machine learning applications require continual learning - where data comes in a sequence of datasets, each is used for training and then permanently discarded. From a Bayesian perspective, continual learning seems straightforward:…

Bayesian field theory denotes a nonparametric Bayesian approach for learning functions from observational data. Based on the principles of Bayesian statistics, a particular Bayesian field theory is defined by combining two models: a…

Big Data often presents as massive non-probability samples. Not only is the selection mechanism often unknown, but larger data volume amplifies the relative contribution of selection bias to total error. Existing bias adjustment approaches…

Robustness analysis is an emerging field in the domain of uncertainty quantification. It consists of analysing the response of a computer model with uncertain inputs to the perturbation of one or several of its input distributions. Thus, a…

Bayesian learning provides a unified skeleton to solve the electrophysiological source imaging task. From this perspective, existing source imaging algorithms utilize the Gaussian assumption for the observation noise to build the likelihood…