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Observational healthcare data offer the potential to estimate causal effects of medical products on a large scale. However, the confidence intervals and p-values produced by observational studies only account for random error and fail to…

Bayesian methods feature useful properties for solving inverse problems, such as tomographic reconstruction. The prior distribution introduces regularization, which helps solving the ill-posed problem and reduces overfitting. In practice,…

Optimization is widely used in statistics, and often efficiently delivers point estimates on useful spaces involving structural constraints or combinatorial structure. To quantify uncertainty, Gibbs posterior exponentiates the negative loss…

Comparing competing mathematical models of complex natural processes is a shared goal among many branches of science. The Bayesian probabilistic framework offers a principled way to perform model comparison and extract useful metrics for…

As modern neural networks get more complex, specifying a model with high predictive performance and sound uncertainty quantification becomes a more challenging task. Despite some promising theoretical results on the true posterior…

This paper considers the problem of making statistical inferences about a parameter when a narrow interval centred at a given value of the parameter is considered special, which is interpreted as meaning that there is a substantial degree…

Generalised Bayesian Inference (GBI) attempts to address model misspecification in a standard Bayesian setup by tempering the likelihood. The likelihood is raised to a fractional power, called the learning rate, which reduces its importance…

Missing time-series data is a prevalent problem in many prescriptive analytics models in operations management, healthcare and finance. Imputation methods for time-series data are usually applied to the full panel data with the purpose of…

Predicting outcomes in external domains is challenging due to hidden confounders that potentially influence both predictors and outcomes. Well-established methods frequently rely on stringent assumptions, explicit knowledge about the…

We propose algorithms for addressing the bias of the posterior mean when used as an estimator of parameters. These algorithms build upon the recently proposed Bayesian infinitesimal jackknife approximation (Giordano and Broderick (2023))…

Deep learning has revolutionized the last decade, being at the forefront of extraordinary advances in a wide range of tasks including computer vision, natural language processing, and reinforcement learning, to name but a few. However, it…

Posterior sampling by Monte Carlo methods provides a more comprehensive solution approach to inverse problems than computing point estimates such as the maximum posterior using optimization methods, at the expense of usually requiring many…

We propose a novel computationally low-cost method for estimating a general predictive measure of generalised Bayesian inference. The proposed method utilises posterior covariance and provides estimators of the Gibbs and the plugin…

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…

Surprise-based learning allows agents to rapidly adapt to non-stationary stochastic environments characterized by sudden changes. We show that exact Bayesian inference in a hierarchical model gives rise to a surprise-modulated trade-off…

Preferential Bayesian optimization allows optimization of objectives that are either expensive or difficult to measure directly, by relying on a minimal number of comparative evaluations done by a human expert. Generating candidate…

A new approximate Bayesian inferential framework is proposed that exploits multiple information sources -- daily spot returns, high-frequency spot data and option prices -- and enables fast calculation of probabilistic predictions of future…

In this article a novel approach for training deep neural networks using Bayesian techniques is presented. The Bayesian methodology allows for an easy evaluation of model uncertainty and additionally is robust to overfitting. These are…

This work proposes a Bayesian inference method for the reduced-order modeling of time-dependent systems. Informed by the structure of the governing equations, the task of learning a reduced-order model from data is posed as a Bayesian…

This paper reviews recent developments in statistical structure learning; namely, Bayesian model reduction. Bayesian model reduction is a method for rapidly computing the evidence and parameters of probabilistic models that differ only in…