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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…

The problem of efficiently generating random samples from high-dimensional and non-log-concave posterior measures arising from nonlinear regression problems is considered. Extending investigations from arXiv:2009.05298, local and global…

It is well-known that the posterior density of linear inverse problems with Gaussian prior and Gaussian likelihood is also Gaussian, hence completely described by its covariance and expectation. Sampling from a Gaussian posterior may be…

Surrogate models are used to alleviate the computational burden in engineering tasks, which require the repeated evaluation of computationally demanding models of physical systems, such as the efficient propagation of uncertainties. For…

Surrogate models provide a quick-to-evaluate approximation to complex computational models and are essential for multi-query problems like design optimisation. The inputs of current deterministic computational models are usually…

We propose a surrogate function for efficient yet principled use of score-based priors in Bayesian imaging. We consider ill-posed inverse imaging problems in which one aims for a clean image posterior given incomplete or noisy measurements.…

In a task where many similar inverse problems must be solved, evaluating costly simulations is impractical. Therefore, replacing the model $y$ with a surrogate model $y_s$ that can be evaluated quickly leads to a significant speedup. The…

Multivariate, heteroscedastic errors complicate statistical inference in many large-scale denoising problems. Empirical Bayes is attractive in such settings, but standard parametric approaches rest on assumptions about the form of the prior…

We study high-dimensional Bayesian linear regression with product priors. Using the nascent theory of non-linear large deviations (Chatterjee and Dembo,2016), we derive sufficient conditions for the leading-order correctness of the naive…

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…

Approximate Bayesian Computation (ABC) is typically used when the likelihood is either unavailable or intractable but where data can be simulated under different parameter settings using a forward model. Despite the recent interest in ABC,…

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…

Due to their conjugate posteriors, Gaussian process priors are attractive for estimating the drift of stochastic differential equations with continuous time observations. However, their performance strongly depends on the choice of the…

We consider the accuracy of an approximate posterior distribution in nonparametric regression problems by combining posterior distributions computed on subsets of the data defined by the locations of the independent variables. We show that…

We derive rates of contraction of posterior distributions on nonparametric models resulting from sieve priors. The aim of the paper is to provide general conditions to get posterior rates when the parameter space has a general structure,…

Generalized linear models (GLMs) are popular for data-analysis in almost all quantitative sciences, but the choice of likelihood family and link function is often difficult. This motivates the search for likelihoods and links that minimize…

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…

Sampling from the posterior distribution poses a major computational challenge in solving inverse problems using latent diffusion models. Common methods rely on Tweedie's first-order moments, which are known to induce a quality-limiting…

We consider least squares estimation in a general nonparametric regression model. The rate of convergence of the least squares estimator (LSE) for the unknown regression function is well studied when the errors are sub-Gaussian. We find…

Popular deterministic approximations of posterior distributions from, e.g. the Laplace method, variational Bayes and expectation-propagation, generally rely on symmetric approximating families, often taken to be Gaussian. This choice…