Related papers: Joint Bayesian separation and restoration of CMB f…
We propose a new approach for the accurate reconstruction of cosmic microwave background distributions from observations containing in addition to the primary fluctuations the radiation from unresolved extragalactic point sources and pixel…
Discrete mixture models are routinely used for density estimation and clustering. While conducting inferences on the cluster-specific parameters, current frequentist and Bayesian methods often encounter problems when clusters are placed too…
We propose an algorithm for the efficient and robust sampling of the posterior probability distribution in Bayesian inference problems. The algorithm combines the local search capabilities of the Manifold Metropolis Adjusted Langevin…
In order to solve tasks like uncertainty quantification or hypothesis tests in Bayesian imaging inverse problems, we often have to draw samples from the arising posterior distribution. For the usually log-concave but high-dimensional…
In many inference problems, the evaluation of complex and costly models is often required. In this context, Bayesian methods have become very popular in several fields over the last years, in order to obtain parameter inversion, model…
Even in low dimensions, sampling from multi-modal distributions is challenging. We provide the first sampling algorithm for a broad class of distributions -- including all Gaussian mixtures -- with a query complexity that is polynomial in…
In this article we consider Bayesian estimation of static parameters for a class of partially observed McKean-Vlasov diffusion processes with discrete-time observations over a fixed time interval. This problem features several obstacles to…
The extraction of foreground and CMB maps from multi-frequency observations relies mostly on the different frequency behavior of the different components. Existing Bayesian methods additionally make use of a Gaussian prior for the CMB whose…
We study the problem of approximate sampling from non-log-concave distributions, e.g., Gaussian mixtures, which is often challenging even in low dimensions due to their multimodality. We focus on performing this task via Markov chain Monte…
We propose a Bayesian inference framework to estimate uncertainties in inverse scattering problems. Given the observed data, the forward model and their uncertainties, we find the posterior distribution over a finite parameter field…
This paper studies a fully Bayesian algorithm for endmember extraction and abundance estimation for hyperspectral imagery. Each pixel of the hyperspectral image is decomposed as a linear combination of pure endmember spectra following the…
Bayesian model selection provides a powerful framework for objectively comparing models directly from observed data, without reference to ground truth data. However, Bayesian model selection requires the computation of the marginal…
Bayesian Positive Source Separation (BPSS) is a useful unsupervised approach for hyperspectral data unmixing, where numerical non-negativity of spectra and abundances has to be ensured, such in remote sensing. Moreover, it is sensible to…
This paper introduces methodology for performing Bayesian inference sequentially on a sequence of posteriors on spaces of different dimensions. We show how this may be achieved through the use of sequential Monte Carlo (SMC) samplers (Del…
We present a sequential sampling methodology for weakly structural Markov laws, arising naturally in a Bayesian structure learning context for decomposable graphical models. As a key component of our suggested approach, we show that the…
Most modern imaging systems incorporate a computational pipeline to infer the image of interest from acquired measurements. The Bayesian approach to solve such ill-posed inverse problems involves the characterization of the posterior…
The problem of Bayesian reduced rank regression is considered in this paper. We propose, for the first time, to use Langevin Monte Carlo method in this problem. A spectral scaled Student prior distrbution is used to exploit the underlying…
Finite mixtures are a cornerstone of Bayesian modelling, and it is well-known that sampling from the resulting posterior distribution can be a hard task. In particular, popular reversible Markov chain Monte Carlo schemes are often slow to…
One of the fundamental tasks of science is to find explainable relationships between observed phenomena. One approach to this task that has received attention in recent years is based on probabilistic graphical modelling with sparsity…
A Bayesian approach is presented for detecting and characterising the signal from discrete objects embedded in a diffuse background. The approach centres around the evaluation of the posterior distribution for the parameters of the discrete…