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We develop a variational Bayes approach for dynamic variable selection in high-dimensional regression models with time-varying parameters and predictors that exhibit a predefined group structure. Through comprehensive simulation studies, we…

Probabilistic regression techniques in control and robotics applications have to fulfill different criteria of data-driven adaptability, computational efficiency, scalability to high dimensions, and the capacity to deal with different…

This article revisits the problem of Bayesian shape-restricted inference in the light of a recently developed approximate Gaussian process that admits an equivalent formulation of the shape constraints in terms of the basis coefficients. We…

Adaptive Bayesian quadrature (ABQ) is a powerful approach to numerical integration that empirically compares favorably with Monte Carlo integration on problems of medium dimensionality (where non-adaptive quadrature is not competitive). Its…

With extreme weather events becoming more common, the risk posed by surface water flooding is ever increasing. In this work we propose a model, and associated Bayesian inference scheme, for generating probabilistic (high-resolution…

There is currently a renewed interest in the Bayesian predictive approach to statistics. This paper offers a review on foundational concepts and focuses on predictive modeling, which by directly reasoning on prediction, bypasses inferential…

We analyze the dynamics of an algorithm for approximate inference with large Gaussian latent variable models in a student-teacher scenario. To model nontrivial dependencies between the latent variables, we assume random covariance matrices…

The standard approach to Bayesian inference is based on the assumption that the distribution of the data belongs to the chosen model class. However, even a small violation of this assumption can have a large impact on the outcome of a…

Mathematical models in computational physics contain uncertain parameters that impact prediction accuracy. In turbulence modeling, this challenge is especially significant: Reynolds averaged Navier-Stokes (RANS) models, such as the…

Fitting statistical models to spatiotemporal data requires finding the right balance between imposing smoothness and following the data. In the context of p-splines, we propose a Bayesian framework for choosing the smoothing parameter which…

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 cubature (BC) is a popular inferential perspective on the cubature of expensive integrands, wherein the integrand is emulated using a stochastic process model. Several approaches have been put forward to encode sequential…

The efficient resolution of Bayesian inverse problems remains challenging due to the high computational cost of traditional sampling methods. In this paper, we propose a novel framework that integrates Conditional Flow Matching (CFM) with a…

A wide variety of battery models are available, and it is not always obvious which model `best' describes a dataset. This paper presents a Bayesian model selection approach using Bayesian quadrature. The model evidence is adopted as the…

Likelihood-based inference in stochastic non-linear dynamical systems, such as those found in chemical reaction networks and biological clock systems, is inherently complex and has largely been limited to small and unrealistically simple…

Fourier feature approximations have been successfully applied in the literature for scalable Gaussian Process (GP) regression. In particular, Quadrature Fourier Features (QFF) derived from Gaussian quadrature rules have gained popularity in…

Neural networks are popular state-of-the-art models for many different tasks.They are often trained via back-propagation to find a value of the weights that correctly predicts the observed data. Although back-propagation has shown good…

Incorporating computational fluid dynamics in the design process of jets, spacecraft, or gas turbine engines is often challenged by the required computational resources and simulation time, which depend on the chosen physics-based…

This article tackles the old problem of prediction via a nonparametric transformation model (NTM) in a new Bayesian way. Estimation of NTMs is known challenging due to model unidentifiability though appealing because of its robust…

Model-form uncertainties in complex mechanics systems are a major obstacle for predictive simulations. Reducing these uncertainties is critical for stake-holders to make risk-informed decisions based on numerical simulations. For example,…