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Mixture models are widely used in Bayesian statistics and machine learning, in particular in computational biology, natural language processing and many other fields. Variational inference, a technique for approximating intractable…
Inverse scattering problems have many important applications. In this paper, given limited aperture data, we propose a Bayesian method for the inverse acoustic scattering to reconstruct the shape of an obstacle. The inverse problem is…
Statistical tasks such as density estimation and approximate Bayesian inference often involve densities with unknown normalising constants. Score-based methods, including score matching, are popular techniques as they are free of…
This work is concerned with the problem of blind source separation and its applications to imaging. We first establish a theoretical result that we stated in our previous article on imaging in diffusive environments. This result is a…
A spectral approach to Bayesian inference is presented. It pursues the emulation of the posterior probability density. The starting point is a series expansion of the likelihood function in terms of orthogonal polynomials. From this…
In astronomy multiple images are frequently obtained at the same position of the sky for follow-up co-addition as it helps one go deeper and look for fainter objects. With large scale panchromatic synoptic surveys becoming more common,…
This is a preliminary version of visual interpretation integrating multiple sensors in SUCCESSOR, an intelligent, model-based vision system. We pursue a thorough integration of hierarchical Bayesian inference with comprehensive physical…
How much does a single image reveal about the environment it was taken in? In this paper, we investigate how much of that information can be retrieved from a foreground object, combined with the background (i.e. the visible part of the…
Data driven modelling is vital to many analyses at collider experiments, however the derived inference of physical properties becomes subject to details of the model fitting procedure. This work brings a principled Bayesian picture, based…
The Bayesian Block algorithm, originally developed for applications in astronomy, can be used to improve the binning of histograms in high energy physics. The visual improvement can be dramatic, as shown here with two simple examples. More…
When a luminous source is extended, its distortions by weak gravitational lensing are richer than a mere combination of magnification and shear. In a recent work, we proposed an elegant formalism based on complex analysis to describe and…
Constraints are a natural choice for prior information in Bayesian inference. In various applications, the parameters of interest lie on the boundary of the constraint set. In this paper, we use a method that implicitly defines a…
These lecture notes highlight the mathematical and computational structure relating to the formulation of, and development of algorithms for, the Bayesian approach to inverse problems in differential equations. This approach is fundamental…
A multilayered particle is illuminated by plane acoustic or electromagnetic waves of one or several frequencies. We consider the inverse scattering problem for the identification of the layers and of the refraction coefficients of the…
This paper considers a Bayesian approach for inclusion detection in nonlinear inverse problems using two known and popular push-forward prior distributions: the star-shaped and level set prior distributions. We analyze the convergence of…
A simple method of phase-and-amplitude extraction is derived that corrects for image blurring induced by partially spatially coherent incident illumination using only a single intensity image as input. The method is based on Fresnel…
One of the biggest problems faced by current and next-generation astronomical surveys is trying to produce large numbers of accurate cross identifications across a range of wavelength regimes with varying data quality and positional…
Photometric redshift estimation is becoming an increasingly important technique, although the currently existing methods present several shortcomings which hinder their application. Here it is shown that most of those drawbacks are…
In this paper we propose a bayesian approach for near-duplicate image detection, and investigate how different probabilistic models affect the performance obtained. The task of identifying an image whose metadata are missing is often…
Geoscientists use observed data to estimate properties of the Earth's interior. This often requires non-linear inverse problems to be solved and uncertainties to be estimated. Bayesian inference solves inverse problems under a probabilistic…