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Recent work has explored transforming data sets into smaller, approximate summaries in order to scale Bayesian inference. We examine a related problem in which the parameters of a Bayesian model are very large and expensive to store in…

By the nature of their construction, many statistical models for extremes result in likelihood functions that are computationally prohibitive to evaluate. This is consequently problematic for the purposes of likelihood-based inference. With…

Inverse problems can be described as limited-data problems in which the signal of interest cannot be observed directly. A physics-based forward model that relates the signal with the observations is typically needed. Unfortunately, unknown…

In the paper, we develop an ensemble-based implicit sampling method for Bayesian inverse problems. For Bayesian inference, the iterative ensemble smoother (IES) and implicit sampling are integrated to obtain importance ensemble samples,…

We present a Newton-like method to solve inverse problems and to quantify parameter uncertainties. We apply the method to parameter reconstruction in optical scatterometry, where we take into account a priori information and measurement…

When solving combinatorial problems, pruning symmetric solution candidates from the search space is essential. Most of the existing approaches are instance-specific and focus on the automatic computation of Symmetry Breaking Constraints…

Inverse problems have many applications in science and engineering. In Computer vision, several image restoration tasks such as inpainting, deblurring, and super-resolution can be formally modeled as inverse problems. Recently, methods have…

This paper is concerned with a lesser-studied problem in the context of model-based, uncertainty quantification (UQ), that of optimization/design/control under uncertainty. The solution of such problems is hindered not only by the usual…

Within the framework of complex system design, it is often necessary to solve mixed variable optimization problems, in which the objective and constraint functions can depend simultaneously on continuous and discrete variables.…

By now Bayesian methods are routinely used in practice for solving inverse problems. In inverse problems the parameter or signal of interest is observed only indirectly, as an image of a given map, and the observations are typically further…

Polynomial chaos expansions are used to reduce the computational cost in the Bayesian solutions of inverse problems by creating a surrogate posterior that can be evaluated inexpensively. We show, by analysis and example, that when the data…

We present a novel technique for tailoring Bayesian quadrature (BQ) to model selection. The state-of-the-art for comparing the evidence of multiple models relies on Monte Carlo methods, which converge slowly and are unreliable for…

Markov chain Monte Carlo (MCMC) methods remain the mainstay of Bayesian estimation of structural equation models (SEM), though they often incur a high computational cost. We present a bespoke approximate Bayesian approach to SEM, drawing on…

Sequential neural posterior estimation (SNPE) techniques have been recently proposed for dealing with simulation-based models with intractable likelihoods. Unlike approximate Bayesian computation, SNPE techniques learn the posterior from…

We propose a new approach to linear ill-posed inverse problems. Our algorithm alternates between enforcing two constraints: the measurements and the statistical correlation structure in some transformed space. We use a non-linear multiscale…

Bayesian inference allows expressing the uncertainty of posterior belief under a probabilistic model given prior information and the likelihood of the evidence. Predominantly, the likelihood function is only implicitly established by a…

In this paper we propose a new Bayesian estimation method to solve linear inverse problems in signal and image restoration and reconstruction problems which has the property to be scale invariant. In general, Bayesian estimators are {\em…

The Bayesian inversion method demonstrates significant potential for solving inverse problems, enabling both point estimation and uncertainty quantification (UQ). However, Bayesian maximum a posteriori (MAP) estimation may become unstable…

We consider the problem of estimating rare event probabilities, focusing on systems whose evolution is governed by differential equations with uncertain input parameters. If the system dynamics is expensive to compute, standard sampling…

Likelihood-free methods, such as approximate Bayesian computation, are powerful tools for practical inference problems with intractable likelihood functions. Markov chain Monte Carlo and sequential Monte Carlo variants of approximate…