Related papers: MAP Estimators for Piecewise Continuous Inversion

A recently developed measure-theoretic framework solves a stochastic inverse problem (SIP) for models where uncertainties in model output data are predominantly due to aleatoric (i.e., irreducible) uncertainties in model inputs (i.e.,…

We derive a maximum a posteriori estimator for the linear observation model, where the signal and noise covariance matrices are both uncertain. The uncertainties are treated probabilistically by modeling the covariance matrices with prior…

This paper is concerned with Bayesian inferential methods for data from controlled branching processes that account for model robustness through the use of disparities. Under regularity conditions, we establish that estimators built on…

We attempt image restoration in the framework of the Baysian inference. Recently, it has been shown that under a certain criterion the MAP (Maximum A Posterior) estimate, which corresponds to the minimization of energy, can be outperformed…

In electroencephalography (EEG) source imaging, the inverse source estimates are depth biased in such a way that their maxima are often close to the sensors. This depth bias can be quantified by inspecting the statistics (mean and…

Bayesian modelling and computational inference by Markov chain Monte Carlo (MCMC) is a principled framework for large-scale uncertainty quantification, though is limited in practice by computational cost when implemented in the simplest…

In this paper we extend a recent idea of formulating and regularizing inverse problems as minimization problems, so without using a forward operator, thus avoiding explicit evaluation of a parameter-to-state map. We do so by rephrasing…

We present a PTAS for computing the maximum a posteriori assignment on Pairwise Markov Random Fields with non-negative weights in planar graphs. This algorithm is practical and not far behind state-of-the-art techniques in image processing.…

The Bayesian methods for linear inverse problems is studied using hierarchical Gaussian models. The problems are considered with different discretizations, and we analyze the phenomena which appear when the discretization becomes finer. A…

One popular approach for blind deconvolution is to formulate a maximum a posteriori (MAP) problem with sparsity priors on the gradients of the latent image, and then alternatingly estimate the blur kernel and the latent image. While several…

A multivariate distribution can be described by a triangular transport map from the target distribution to a simple reference distribution. We propose Bayesian nonparametric inference on the transport map by modeling its components using…

We consider geothermal inverse problems and uncertainty quantification from a Bayesian perspective. Our main goal is to make standard, `out-of-the-box' Markov chain Monte Carlo (MCMC) sampling more feasible for complex simulation models by…

In this paper we consider Bayesian estimation for the parameters of inverse Gaussian distribution. Our emphasis is on Markov Chain Monte Carlo methods. We provide complete implementation of the Gibbs sampler algorithm. Assuming an…

We present a novel probabilistic approach for generating multi-fidelity data while accounting for errors inherent in both low- and high-fidelity data. In this approach a graph Laplacian constructed from the low-fidelity data is used to…

This paper presents a new Expectation Propagation (EP) framework for image restoration using patch-based prior distributions. While Monte Carlo techniques are classically used to sample from intractable posterior distributions, they can…

Accelerating magnetic resonance imaging (MRI) remains challenging, particularly under realistic acquisition noise. While diffusion models have recently shown promise for reconstructing undersampled MRI data, many approaches lack an explicit…

Sum-product networks (SPNs) are a class of probabilistic graphical models that allow tractable marginal inference. However, the maximum a posteriori (MAP) inference in SPNs is NP-hard. We investigate MAP inference in SPNs from both…

Recent studies demonstrate that diffusion models can serve as a strong prior for solving inverse problems. A prominent example is Diffusion Posterior Sampling (DPS), which approximates the posterior distribution of data given the measure…

In this paper, we present a comprehensive analysis of the posterior covariance field in Gaussian processes, with applications to the posterior covariance matrix. The analysis is based on the Gaussian prior covariance but the approach also…

There is a wide range of applications where the local extrema of a function are the key quantity of interest. However, there is surprisingly little work on methods to infer local extrema with uncertainty quantification in the presence of…