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Computer models, aiming at simulating a complex real system, are often calibrated in the light of data to improve performance. Standard calibration methods assume that the optimal values of calibration parameters are invariant to the model…

Many models of interest in the natural and social sciences have no closed-form likelihood function, which means that they cannot be treated using the usual techniques of statistical inference. In the case where such models can be…

Gaussian graphical models provide a powerful framework to reveal the conditional dependency structure between multivariate variables. The process of uncovering the conditional dependency network is known as structure learning. Bayesian…

Bayesian model selection is premised on the assumption that the data are generated from one of the postulated models. However, in many applications, all of these models are incorrect (that is, there is misspecification). When the models are…

Probabilistic vehicle trajectory prediction is essential for robust safety of autonomous driving. Current methods for long-term trajectory prediction cannot guarantee the physical feasibility of predicted distribution. Moreover, their…

We consider heteroscedastic nonparametric regression models, when both the mean function and variance function are unknown and to be estimated with nonparametric approaches. We derive convergence rates of posterior distributions for this…

Bayesian methods are actively used for parameter identification and uncertainty quantification when solving nonlinear inverse problems with random noise. However, there are only few theoretical results justifying the Bayesian approach.…

A Bayesian non-parametric framework for studying time-to-event data is proposed, where the prior distribution is allowed to depend on an additional random source, and may update with the sample size. Such scenarios are natural, for…

Distribution regression has recently attracted much interest as a generic solution to the problem of supervised learning where labels are available at the group level, rather than at the individual level. Current approaches, however, do not…

In computational inverse problems, it is common that a detailed and accurate forward model is approximated by a computationally less challenging substitute. The model reduction may be necessary to meet constraints in computing time when…

We propose a new method for conducting Bayesian prediction that delivers accurate predictions without correctly specifying the unknown true data generating process. A prior is defined over a class of plausible predictive models. After…

Envelope models provide a sufficient dimension reduction framework for multivariate regression analysis. Bayesian inference for these models has been developed primarily using Markov chain Monte Carlo (MCMC) methods. Specifically, Gibbs…

We propose a novel approach to approximate Bayesian computation (ABC) that seeks to cater for possible misspecification of the assumed model. This new approach can be equally applied to rejection-based ABC and to popular regression…

The estimation of unknown parameters in nonlinear partial differential equations (PDEs) offers valuable insights across a wide range of scientific domains. In this work, we focus on estimating plant root parameters in the Richards equation,…

The representation of the approximate posterior is a critical aspect of effective variational autoencoders (VAEs). Poor choices for the approximate posterior have a detrimental impact on the generative performance of VAEs due to the…

Maximum a posteriori (MAP) estimation, like all Bayesian methods, depends on prior assumptions. These assumptions are often chosen to promote specific features in the recovered estimate. The form of the chosen prior determines the shape of…

Many modern experiments, such as microarray gene expression and genome-wide association studies, present the problem of estimating a large number of parallel effects. Bayesian inference is a popular approach for analyzing such data by…

We study nonparametric Bayesian binary classification, in the case where the unknown probability response function is possibly spatially inhomogeneous, for example, being generally flat across the domain but presenting localized sharp…

We consider the problem of learning a conditional Gaussian graphical model in the presence of latent variables. Building on recent advances in this field, we suggest a method that decomposes the parameters of a conditional Markov random…

The Bayesian paradigm has the potential to solve core issues of deep neural networks such as poor calibration and data inefficiency. Alas, scaling Bayesian inference to large weight spaces often requires restrictive approximations. In this…