Related papers: A Gaussian process and linear-based framework for …
Gaussian process regression is widely applied in computational science and engineering for surrogate modeling owning to its kernel-based and probabilistic nature. In this work, we propose a Bayesian approach that integrates the variability…
Bayesian methods for learning Gaussian graphical models offer a principled framework for quantifying model uncertainty and incorporating prior knowledge. However, their scalability is constrained by the computational cost of jointly…
Background: Continuous traits evolution of a group of taxa that are correlated through a phylogenetic tree is commonly modelled using parametric stochastic differential equations to represent deterministic change of trait through time,…
Computer models are used as a way to explore complex physical systems. Stationary Gaussian process emulators, with their accompanying uncertainty quantification, are popular surrogates for computer models. However, many computer models are…
High dimensional statistics deals with the challenge of extracting structured information from complex model settings. Compared with the growing number of frequentist methodologies, there are rather few theoretically optimal Bayes methods…
Reliable predictive uncertainty estimation plays an important role in enabling the deployment of neural networks to safety-critical settings. A popular approach for estimating the predictive uncertainty of neural networks is to define a…
Estimation of parameters that obey specific constraints is crucial in statistics and machine learning; for example, when parameters are required to satisfy boundedness, monotonicity, or linear inequalities. Traditional approaches impose…
Computing the distribution of trajectories from a Gaussian Process model of a dynamical system is an important challenge in utilizing such models. Motivated by the computational cost of sampling-based approaches, we consider approximations…
Ordinary differential equation (ODE) models are widely used to describe systems in many areas of science. To ensure these models provide accurate and interpretable representations of real-world dynamics, it is often necessary to infer…
Inverse problems, i.e., estimating parameters of physical models from experimental data, are ubiquitous in science and engineering. The Bayesian formulation is the gold standard because it alleviates ill-posedness issues and quantifies…
We present a Bayesian methodology for infinite as well as finite dimensional parameter identification for partial differential equation models. The Bayesian framework provides a rigorous mathematical framework for incorporating prior…
Large neural networks trained on large datasets have become the dominant paradigm in machine learning. These systems rely on maximum likelihood point estimates of their parameters, precluding them from expressing model uncertainty. This may…
Bayesian learning is a powerful learning framework which combines the external information of the data (background information) with the internal information (training data) in a logically consistent way in inference and prediction. By…
A new algorithm is developed to tackle the issue of sampling non-Gaussian model parameter posterior probability distributions that arise from solutions to Bayesian inverse problems. The algorithm aims to mitigate some of the hurdles faced…
This paper addresses the Bayesian calibration of dynamic models with parametric and structural uncertainties, in particular where the uncertain parameters are unknown/poorly known spatio-temporally varying subsystem models. Independent…
In the usual Bayesian setting, a full probabilistic model is required to link the data and parameters, and the form of this model and the inference and prediction mechanisms are specified via de Finetti's representation. In general, such a…
A method for sequential inference of the fixed parameters of a dynamic latent Gaussian models is proposed and evaluated that is based on the iterated Laplace approximation. The method provides a useful trade-off between computational…
We consider the situation where a temporal process is composed of contiguous segments with differing slopes and replicated noise-corrupted time series measurements are observed. The unknown mean of the data generating process is modelled as…
In this article, an overview of Bayesian methods for sequential simulation from posterior distributions of nonlinear and non-Gaussian dynamic systems is presented. The focus is mainly laid on sequential Monte Carlo methods, which are based…
Bayesian Neural Networks provide a principled framework for uncertainty quantification by modeling the posterior distribution of network parameters. However, exact posterior inference is computationally intractable, and widely used…