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In the Bayesian approach to inverse problems, data are often informative, relative to the prior, only on a low-dimensional subspace of the parameter space. Significant computational savings can be achieved by using this subspace to…
We present a Bayesian approach to estimate the parameters of mathematical models of cardiac electrophysiology with quantified uncertainty. Such models capture the dynamics of the electrical signal that coordinates the muscle cell…
A Bayesian approach to nonlinear inverse problems is considered where the unknown quantity (input) is a random spatial field. The forward model is complex and non-linear, therefore computationally expensive. An emulator-based methodology is…
This paper deals with the estimation of the unknown distribution of hidden random variables from the observation of pairwise comparisons between these variables. This problem is inspired by recent developments on Bradley-Terry models in…
In Computational Fluid Dynamics (CFD) studies composed of the coupling of different simulations, the uncertainty in one stage may be propagated to the following stage and affect the accuracy of the prediction. In this paper, a framework for…
Performing stochastic inversion on a computationally expensive forward simulation model with a high-dimensional uncertain parameter space (e.g. a spatial random field) is computationally prohibitive even with gradient information provided.…
We consider Bayesian inverse problems arising in data assimilation for dynamical systems governed by partial and stochastic partial differential equations. The space-time dependent field is inferred jointly with static parameters of the…
Sample-based Bayesian inference provides a route to uncertainty quantification in the geosciences, and inverse problems in general, though is very computationally demanding in the naive form that requires simulating an accurate computer…
In this study, the applicability of generalized polynomial chaos (gPC) expansion for land surface model parameter estimation is evaluated. We compute the (posterior) distribution of the critical hydrological parameters that are subject to…
We propose a Bayesian framework for the received-signal-strength-based cooperative localization problem with unknown path loss exponent. Our purpose is to infer the marginal posterior of each unknown parameter: the position or the path loss…
A new method is proposed for estimating the rate of fugitive emissions of particulate matter from multiple time-dependent sources via measurements of deposition and concentration. We cast this source inversion problem within the Bayesian…
This work presents a detailed mathematical model combined with an innovative efficient numerical model to predict heat, air and moisture transfer through porous building materials. The model considers the transient effects of air transport…
In this work, we investigate the use of Besov priors in the context of Bayesian inverse problems. The solution to Bayesian inverse problems is the posterior distribution which naturally enables us to interpret the uncertainties. Besov…
In computational mechanics, multiple models are often present to describe a physical system. While Bayesian model selection is a helpful tool to compare these models using measurement data, it requires the computationally expensive…
We investigate solution methods for large-scale inverse problems governed by partial differential equations (PDEs) via Bayesian inference. The Bayesian framework provides a statistical setting to infer uncertain parameters from noisy…
In this article, we propose a novel method for sampling potential functions based on noisy observation data of a finite number of observables in quantum canonical ensembles, which leads to the accurate sampling of a wide class of test…
Through the Bayesian lens of data assimilation, uncertainty on model parameters is traditionally quantified through the posterior covariance matrix. However, in modern settings involving high-dimensional and computationally expensive…
Current methods for learning graphical models with latent variables and a fixed structure estimate optimal values for the model parameters. Whereas this approach usually produces overfitting and suboptimal generalization performance,…
Bayesian methods feature useful properties for solving inverse problems, such as tomographic reconstruction. The prior distribution introduces regularization, which helps solving the ill-posed problem and reduces overfitting. In practice,…
As a Bayesian approach to fitting motorway traffic flow models remains rare in the literature, we explore empirically the sampling challenges this approach offers which have to do with the strong correlations and multi-modality of the…