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Incorporating a deep generative model as the prior distribution in inverse problems has established substantial success in reconstructing images from corrupted observations. Notwithstanding, the existing optimization approaches use gradient…
We consider the problem of optimizing a real-valued continuous function $f$ using a Bayesian approach, where the evaluations of $f$ are chosen sequentially by combining prior information about $f$, which is described by a random process…
In this article we develop a new sequential Monte Carlo (SMC) method for multilevel (ML) Monte Carlo estimation. In particular, the method can be used to estimate expectations with respect to a target probability distribution over an…
Developing efficient Bayesian computation algorithms for imaging inverse problems is challenging due to the dimensionality involved and because Bayesian imaging models are often not smooth. Current state-of-the-art methods often address…
Sequential Monte Carlo (SMC) methods have recently shown successful results for conditional sampling of generative diffusion models. In this paper we propose a new diffusion posterior SMC sampler achieving improved statistical efficiencies,…
Inverse problems are prevalent in both scientific research and engineering applications. In the context of Bayesian inverse problems, sampling from the posterior distribution can be particularly challenging when the forward models are…
The Bayesian approach to inverse problems typically relies on posterior sampling approaches, such as Markov chain Monte Carlo, for which the generation of each sample requires one or more evaluations of the parameter-to-observable map or…
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…
Inverse problems involving partial differential equations (PDEs) are widely used in science and engineering. Although such problems are generally ill-posed, different regularisation approaches have been developed to ameliorate this problem.…
Markov chain Monte Carlo (MCMC) algorithms have become powerful tools for Bayesian inference. However, they do not scale well to large-data problems. Divide-and-conquer strategies, which split the data into batches and, for each batch, run…
Sequential Monte Carlo (SMC) methods comprise one of the most successful approaches to approximate Bayesian filtering. However, SMC without good proposal distributions struggle in high dimensions. We propose nested sequential Monte Carlo…
We propose a multilevel Monte Carlo-FEM algorithm to solve elliptic Bayesian inverse problems with "Besov random tree prior". These priors are given by a wavelet series with stochastic coefficients, and certain terms in the expansion…
In the field of inverse estimation for systems modeled by partial differential equations (PDEs), challenges arise when estimating high- (or even infinite-) dimensional parameters. Typically, the ill-posed nature of such problems…
We consider the problem of estimating expectations with respect to a target distribution with an unknown normalizing constant, and where even the unnormalized target needs to be approximated at finite resolution. Under such an assumption,…
We consider the inverse problem of estimating the initial condition of a partial differential equation, which is only observed through noisy measurements at discrete time intervals. In particular, we focus on the case where Eulerian…
Bayesian estimation methods for sparse blind deconvolution problems conventionally employ Bernoulli-Gaussian (BG) prior for modeling sparse sequences and utilize Markov Chain Monte Carlo (MCMC) methods for the estimation of unknowns.…
Bayesian neural learning feature a rigorous approach to estimation and uncertainty quantification via the posterior distribution of weights that represent knowledge of the neural network. This not only provides point estimates of optimal…
Approximate Bayesian computation (ABC) methods are standard tools for inferring parameters of complex models when the likelihood function is analytically intractable. A popular approach to improving the poor acceptance rate of the basic…
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…
Sequential Monte Carlo (SMC) methods are a class of Monte Carlo methods that are used to obtain random samples of a high dimensional random variable in a sequential fashion. Many problems encountered in applications often involve different…