Related papers: Joint Bayesian separation and restoration of CMB f…

Despite recent advances, sampling-based inference for Bayesian Neural Networks (BNNs) remains a significant challenge in probabilistic deep learning. While sampling-based approaches do not require a variational distribution assumption,…

Diffusion models (DMs) have emerged as powerful image priors in Bayesian computational imaging. Two primary strategies have been proposed for leveraging DMs in this context: Plug-and-Play methods, which are zero-shot and highly flexible but…

The problem of joint estimation of multiple graphical models from high dimensional data has been studied in the statistics and machine learning literature, due to its importance in diverse fields including molecular biology, neuroscience…

This paper presents an unsupervised method that trains neural source separation by using only multichannel mixture signals. Conventional neural separation methods require a lot of supervised data to achieve excellent performance. Although…

We review the use of Bayesian Model Averaging in astrophysics. We first introduce the statistical basis of Bayesian Model Selection and Model Averaging. We discuss methods to calculate the model-averaged posteriors, including Markov Chain…

Generative diffusions are a powerful class of Monte Carlo samplers that leverage bridging Markov processes to approximate complex, high-dimensional distributions, such as those found in image processing and language models. Despite their…

A recent line of research has exploited pre-trained generative diffusion models as priors for solving Bayesian inverse problems. We contribute to this research direction by designing a sequential Monte Carlo method for linear-Gaussian…

We present Bayesian techniques for solving inverse problems which involve mean-square convergent random approximations of the forward map. Noisy approximations of the forward map arise in several fields, such as multiscale problems and…

This paper presents an improved implicit sampling method for hierarchical Bayesian inverse problems. A widely used approach for sampling posterior distribution is based on Markov chain Monte Carlo (MCMC). However, the samples generated by…

We consider the situation where a temporal process is composed of contiguous segments with differing slopes and replicated noise-corrupted time series measurements are observed. The unknown mean of the data generating process is modelled as…

This paper presents a Markov chain Monte Carlo method to generate approximate posterior samples in retrospective multiple changepoint problems where the number of changes is not known in advance. The method uses conjugate models whereby the…

Astronomical images in the Poisson regime are typically characterized by a spatially varying cosmic background, large variety of source morphologies and intensities, data incompleteness, steep gradients in the data, and few photon counts…

In this contribution, we present new algorithms to source separation for the case of noisy instantaneous linear mixture, within the Bayesian statistical framework. The source distribution prior is modeled by a mixture of Gaussians…

this paper we consider the problem of separating noisy instantaneous linear mixtures of document images in the Bayesian framework. The source image is modeled hierarchically by a latent labeling process representing the common…

Bayesian methods of sampling from a posterior distribution are becoming increasingly popular due to their ability to precisely display the uncertainty of a model fit. Classical methods based on iterative random sampling and posterior…

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…

This paper addresses the problem of summarizing the posterior distributions that typically arise, in a Bayesian framework, when dealing with signal decomposition problems with unknown number of components. Such posterior distributions are…

We present a Bayesian inference approach to estimating the cumulative mass profile and mean squared velocity profile of a globular cluster given the spatial and kinematic information of its stars. Mock globular clusters with a range of…

Denoising diffusion models have driven significant progress in the field of Bayesian inverse problems. Recent approaches use pre-trained diffusion models as priors to solve a wide range of such problems, only leveraging inference-time…

Bayesian models have become very popular over the last years in several fields such as signal processing, statistics, and machine learning. Bayesian inference requires the approximation of complicated integrals involving posterior…