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High-throughput characterization often requires estimating parameters and model dimension from experimental data of limited quantity and quality. Such data may result in an ill-posed inverse problem, where multiple sets of parameters and…

In the following article we consider approximate Bayesian parameter inference for observation driven time series models. Such statistical models appear in a wide variety of applications, including econometrics and applied mathematics. This…

Bayesian analyses combine information represented by different terms in a joint Bayesian model. When one or more of the terms is misspecified, it can be helpful to restrict the use of information from suspect model components to modify…

This book aims to provide a graduate-level introduction to advanced topics in Markov chain Monte Carlo (MCMC) algorithms, as applied broadly in the Bayesian computational context. Most, if not all of these topics (stochastic gradient MCMC,…

We introduce a framework for efficient Markov Chain Monte Carlo (MCMC) algorithms targeting discrete-valued high-dimensional distributions, such as posterior distributions in Bayesian variable selection (BVS) problems. We show that many…

Specifying a full Bayesian model that integrates multiple data sources can be challenging. One natural approach is to specify each individual model separately and join them afterwards. This is the approach adopted in Markov melding.…

In recent years, methods for Bayesian inference have been widely used in many different problems in physics where detection and characterization are necessary. Data analysis in gravitational-wave astronomy is a prime example of such a case.…

In recent years, a wide range of mortality models has been proposed to address the diverse factors influencing mortality rates, which has highlighted the need to perform model selection. Traditional mortality model selection methods, such…

Estimation and prediction in high dimensional multivariate factor stochastic volatility models is an important and active research area because such models allow a parsimonious representation of multivariate stochastic volatility. Bayesian…

This work introduces a new method designed for Bayesian deep learning called scalable Bayesian Monte Carlo (SBMC). The method is comprised of a model and an algorithm. The model interpolates between a point estimator and the posterior. The…

Calibration of individual based models (IBMs), successful in modeling complex ecological dynamical systems, is often performed only ad-hoc. Bayesian inference can be used for both parameter estimation and uncertainty quantification, but its…

Even though Bayesian neural networks offer a promising framework for modeling uncertainty, active learning and incorporating prior physical knowledge, few applications of them can be found in the context of interatomic force modeling. One…

Inverse problems involving partial differential equations (PDEs) are widely used in science and engineering. Although such problems are generally ill-posed, different regularisation approaches have been developed to ameliorate this problem.…

Decision trees are flexible models that are well suited for many statistical regression problems. In a Bayesian framework for regression trees, Markov Chain Monte Carlo (MCMC) search algorithms are required to generate samples of tree…

The Markov Decision Process (MDP) is a popular framework for sequential decision-making problems, and uncertainty quantification is an essential component of it to learn optimal decision-making strategies. In particular, a Bayesian…

Bayesian nonparametric inferential procedures based on Markov chain Monte Carlo marginal methods typically yield point estimates in the form of posterior expectations. Though very useful and easy to implement in a variety of statistical…

Estimating the predictive uncertainty of a Bayesian learning model is critical in various decision-making problems, e.g., reinforcement learning, detecting adversarial attack, self-driving car. As the model posterior is almost always…

Bayesian feature allocation models are a popular tool for modelling data with a combinatorial latent structure. Exact inference in these models is generally intractable and so practitioners typically apply Markov Chain Monte Carlo (MCMC)…

Modern imaging methods rely strongly on Bayesian inference techniques to solve challenging imaging problems. Currently, the predominant Bayesian computation approach is convex optimisation, which scales very efficiently to high dimensional…

Statistical models can involve implicitly defined quantities, such as solutions to nonlinear ordinary differential equations (ODEs), that unavoidably need to be numerically approximated in order to evaluate the model. The approximation…