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State-space models (SSMs) are powerful probabilistic tools for modeling time-varying systems with latent dynamics. Inference in SSMs involves the estimation of latent states and parameters. In this work, we focus on parameter inference,…

Nested sampling is a simulation method for approximating marginal likelihoods proposed by Skilling (2006). We establish that nested sampling has an approximation error that vanishes at the standard Monte Carlo rate and that this error is…

Nested sampling is an important tool for conducting Bayesian analysis in Astronomy and other fields, both for sampling complicated posterior distributions for parameter inference, and for computing marginal likelihoods for model comparison.…

Bayesian inference promises a framework for principled uncertainty quantification of neural network predictions. Barriers to adoption include the difficulty of fully characterizing posterior distributions on network parameters and the…

Reconstructing pathogen dynamics from genetic data as they become available during an outbreak or epidemic represents an important statistical scenario in which observations arrive sequentially in time and one is interested in performing…

Both linear mixed models (LMMs) and sparse regression models are widely used in genetics applications, including, recently, polygenic modeling in genome-wide association studies. These two approaches make very different assumptions, so are…

Bayesian Neural Networks (BNNs) offer a principled and natural framework for proper uncertainty quantification in the context of deep learning. They address the typical challenges associated with conventional deep learning methods, such as…

Inverse problems and, in particular, inferring unknown or latent parameters from data are ubiquitous in engineering simulations. A predominant viewpoint in identifying unknown parameters is Bayesian inference where both prior information…

Bayesian inference in deep neural networks is challenging due to the high-dimensional, strongly multi-modal parameter posterior density landscape. Markov chain Monte Carlo approaches asymptotically recover the true posterior but are…

Ensembles of neural networks (NNs) have long been used to estimate predictive uncertainty; a small number of NNs are trained from different initialisations and sometimes on differing versions of the dataset. The variance of the ensemble's…

Estimating the parameters of mathematical models is a common problem in almost all branches of science. However, this problem can prove notably difficult when processes and model descriptions become increasingly complex and an explicit…

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…

It is very challenging to select informative features from tens of thousands of measured features in high-throughput data analysis. Recently, several parametric/regression models have been developed utilizing the gene network information to…

We develop Bayesian predictive stacking for geostatistical models, where the primary inferential objective is to provide inference on the latent spatial random field and conduct spatial predictions at arbitrary locations. We exploit…

Deep Gaussian processes provide a flexible approach to probabilistic modelling of data using either supervised or unsupervised learning. For tractable inference approximations to the marginal likelihood of the model must be made. The…

In the case of informative sampling the sampling scheme explicitly or implicitly depends on the response variable. As a result, the sample distribution of response variable can- not be used for making inference about the population. In this…

Bayesian networks (BNs) are probabilistic graphical models for describing complex joint probability distributions. The main problem for BNs is inference: Determine the probability of an event given observed evidence. Since exact inference…

In Bayesian phylogenetics, our goal is to estimate the posterior distribution over phylogenetic trees. Markov chain Monte Carlo methods are widely used to approximate the phylogenetic posterior distributions. For large-scale sequence data,…

This paper considers the problem of model selection within the context of finite element model updating. Given that a number of FEM updating models, with different updating parameters, can be designed, this paper proposes using the Bayesian…

Neural networks (NNs) are primarily developed within the frequentist statistical framework. Nevertheless, frequentist NNs lack the capability to provide uncertainties in the predictions, and hence their robustness can not be adequately…