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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…
Bayesian learning in undirected graphical models|computing posterior distributions over parameters and predictive quantities is exceptionally difficult. We conjecture that for general undirected models, there are no tractable MCMC (Markov…
We study linear models under heavy-tailed priors from a probabilistic viewpoint. Instead of computing a single sparse most probable (MAP) solution as in standard deterministic approaches, the focus in the Bayesian compressed sensing…
In Bayesian inverse problems, it is common to consider several hyperparameters that define the prior and the noise model that must be estimated from the data. In particular, we are interested in linear inverse problems with additive…
A natural way to quantify uncertainties in Gaussian mixture models (GMMs) is through Bayesian methods. That said, sampling from the joint posterior distribution of GMMs via standard Markov chain Monte Carlo (MCMC) imposes several…
Undirected graphical models are widely used in statistics, physics and machine vision. However Bayesian parameter estimation for undirected models is extremely challenging, since evaluation of the posterior typically involves the…
Mapping with uncertainty representation is required in many research domains, especially for localization. Although there are many investigations regarding the uncertainty of the pose estimation of an ego-robot with map information, the…
We consider the use of Gaussian process (GP) priors for solving inverse problems in a Bayesian framework. As is well known, the computational complexity of GPs scales cubically in the number of datapoints. We here show that in the context…
In this article a novel approach for training deep neural networks using Bayesian techniques is presented. The Bayesian methodology allows for an easy evaluation of model uncertainty and additionally is robust to overfitting. These are…
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…
The Bayesian formulation of inverse problems is attractive for three primary reasons: it provides a clear modelling framework; means for uncertainty quantification; and it allows for principled learning of hyperparameters. The posterior…
Gaussian processes scale prohibitively with the size of the dataset. In response, many approximation methods have been developed, which inevitably introduce approximation error. This additional source of uncertainty, due to limited…
In computational inverse problems, it is common that a detailed and accurate forward model is approximated by a computationally less challenging substitute. The model reduction may be necessary to meet constraints in computing time when…
Researchers increasingly wish to estimate time-varying parameter (TVP) regressions which involve a large number of explanatory variables. Including prior information to mitigate over-parameterization concerns has led to many using Bayesian…
Bayesian optimisation requires fitting a Gaussian process model, which in turn requires specifying prior on the unknown black-box function -- most of the theoretical literature assumes this prior is known. However, it is common to have more…
Many inverse problems include nuisance parameters which, while not of direct interest, are required to recover primary parameters. Structure present in these problems allows efficient optimization strategies - a well known example is…
In this work, we describe a Bayesian framework for reconstructing the boundaries of piecewise smooth regions in the X-ray computed tomography (CT) problem in an infinite-dimensional setting. In addition to the reconstruction, we are also…
The formulation of Bayesian inverse problems involves choosing prior distributions; choices that seem equally reasonable may lead to significantly different conclusions. We develop a computational approach to better understand the impact of…
We provide a complete framework for performing infinite-dimensional Bayesian inference and uncertainty quantification for image reconstruction with Poisson data. In particular, we address the following issues to make the Bayesian framework…
In ill-posed inverse problems, it is commonly desirable to obtain insight into the full spectrum of plausible solutions, rather than extracting only a single reconstruction. Information about the plausible solutions and their likelihoods is…