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In this paper we develop a Bayesian procedure for estimating multivariate stochastic volatility (MSV) using state space models. A multiplicative model based on inverted Wishart and multivariate singular beta distributions is proposed for…

We introduce a flexible empirical Bayes approach for fitting Bayesian generalized linear models. Specifically, we adopt a novel mean-field variational inference (VI) method and the prior is estimated within the VI algorithm, making the…

Spatial generalized linear mixed-effects models are popularly used to analyze spatially indexed univariate responses. However, with modern technology, it is common to observe vector-valued mixed-type responses, e.g., a combination of…

Non-linear hierarchical models are commonly used in many disciplines. However, inference in the presence of non-nested effects and on large datasets is challenging and computationally burdensome. This paper provides two contributions to…

We propose a fast inference method for Bayesian nonlinear support vector machines that leverages stochastic variational inference and inducing points. Our experiments show that the proposed method is faster than competing Bayesian…

Few Bayesian methods for analyzing high-dimensional sparse survival data provide scalable variable selection, effect estimation and uncertainty quantification. Such methods often either sacrifice uncertainty quantification by computing…

Standard simultaneous autoregressive (SAR) models typically assume normally distributed errors, an assumption often violated in real-world datasets that frequently exhibit non-normal, skewed, or heavy-tailed characteristics. New SAR models…

We develop a fast variational approximation scheme for Gaussian process (GP) regression, where the spectrum of the covariance function is subjected to a sparse approximation. Our approach enables uncertainty in covariance function…

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…

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.…

This paper presents a new Bayesian estimation technique for hidden Potts-Markov random fields with unknown regularisation parameters, with application to fast unsupervised K-class image segmentation. The technique is derived by first…

High dimensional vector autoregressive (VAR) models require a large number of parameters to be estimated and may suffer of inferential problems. We propose a new Bayesian nonparametric (BNP) Lasso prior (BNP-Lasso) for high-dimensional VAR…

Recent variational Bayes methods for geospatial regression, proposed as an alternative to computationally expensive Markov chain Monte Carlo (MCMC) sampling, have leveraged Nearest Neighbor Gaussian processes (NNGP) to achieve scalability.…

High-dimensional vector autoregressive (VAR) models provide a flexible framework for characterizing dynamic dependence in multivariate spatio-temporal systems, but their unrestricted estimation becomes infeasible when multiple variables are…

Bayesian predictive inference propagates parameter uncertainty to quantities of interest through the posterior-predictive distribution. In practice, this is typically performed using a two-stage procedure: first approximating the posterior…

Variable selection techniques have become increasingly popular amongst statisticians due to an increased number of regression and classification applications involving high-dimensional data where we expect some predictors to be unimportant.…

We develop a fast and accurate grouped penalized credible region approach for variable selection and prediction in Bayesian high-dimensional linear regression. Most existing Bayesian methods either are subject to high computational costs…

Spatial transcriptomics has revolutionized tissue analysis by simultaneously mapping gene expression, spatial topography, and histological context across consecutive tissue sections, enabling systematic investigation of spatial…

We propose a fast and theoretically grounded method for Bayesian variable selection and model averaging in latent variable regression models. Our framework addresses three interrelated challenges: (i) intractable marginal likelihoods, (ii)…

We develop a Bayesian methodology aimed at simultaneously estimating low-rank and row-sparse matrices in a high-dimensional multiple-response linear regression model. We consider a carefully devised shrinkage prior on the matrix of…