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In the last few decades, Markov chain Monte Carlo (MCMC) methods have been widely applied to Bayesian updating of structural dynamic models in the field of structural health monitoring. Recently, several MCMC algorithms have been developed…

Meta-analysis is widely used to integrate results from multiple experiments to obtain generalized insights. Since meta-analysis datasets are often heteroscedastic due to varying subgroups and temporal heterogeneity arising from experiments…

We analyse and explain the increased generalisation performance of iterate averaging using a Gaussian process perturbation model between the true and batch risk surface on the high dimensional quadratic. We derive three phenomena…

This article describes a full Bayesian treatment for simultaneous fixed-effect selection and parameter estimation in high-dimensional generalized linear mixed models. The approach consists of using a Bayesian adaptive Lasso penalty for…

Recent works propose using the discriminator of a GAN to filter out unrealistic samples of the generator. We generalize these ideas by introducing the implicit Metropolis-Hastings algorithm. For any implicit probabilistic model and a target…

The performance of Gaussian Process (GP) regression is often hampered by the curse of dimensionality, which inflates computational cost and reduces predictive power in high-dimensional problems. Variable selection is thus crucial for…

We develop a Bayesian approach called Bayesian projected calibration to address the problem of calibrating an imperfect computer model using observational data from a complex physical system. The calibration parameter and the physical…

Developments in Deep Learning have significantly improved time series forecasting by enabling more accurate modeling of complex temporal dependencies inherent in sequential data. The effectiveness of such models is often demonstrated on…

This paper introduces a new sparse spatio-temporal structured Gaussian process regression framework for online and offline Bayesian inference. This is the first framework that gives a time-evolving representation of the interdependencies…

We introduce a novel Bayesian approach for variable selection using Gaussian process regression, which is crucial for enhancing interpretability and model regularization. Our method employs nearest neighbor Gaussian processes, serving as…

The Bayesian approach to inverse problems typically relies on posterior sampling approaches, such as Markov chain Monte Carlo, for which the generation of each sample requires one or more evaluations of the parameter-to-observable map or…

We study the nonparametric covariance estimation of a stationary Gaussian field X observed on a regular lattice. In the time series setting, some procedures like AIC are proved to achieve optimal model selection among autoregressive models.…

The usefulness of Bayesian models for density and cluster estimation is well established across multiple literatures. However, there is still a known tension between the use of simpler, more interpretable models and more flexible, complex…

To address the common problem of high dimensionality in tensor regressions, we introduce a generalized tensor random projection method that embeds high-dimensional tensor-valued covariates into low-dimensional subspaces with minimal loss of…

This article introduces a nonparametric approach to spectral analysis of a high-dimensional multivariate nonstationary time series. The procedure is based on a novel frequency-domain factor model that provides a flexible yet parsimonious…

Recently developed adaptive Markov chain Monte Carlo (MCMC) methods have been applied successfully to many problems in Bayesian statistics. Grapham is a new open source implementation covering several such methods, with emphasis on…

We present a new adaptive method for electronic structure calculations based on novel fast algorithms for reduction of multivariate mixtures. In our calculations, spatial orbitals are maintained as Gaussian mixtures whose terms are selected…

In multivariate time series analysis, understanding the underlying causal relationships among variables is often of interest for various applications. Directed acyclic graphs (DAGs) provide a powerful framework for representing causal…

We introduce an adaptive output-sensitive Metropolis-Hastings algorithm for probabilistic models expressed as programs, Adaptive Lightweight Metropolis-Hastings (AdLMH). The algorithm extends Lightweight Metropolis-Hastings (LMH) by…

Scientists often express their understanding of the world through a computationally demanding simulation program. Analyzing the posterior distribution of the parameters given observations (the inverse problem) can be extremely challenging.…