Related papers: A Bayesian thinning algorithm for the point source…

A new strategy based on numerical homogenization and Bayesian techniques for solving multiscale inverse problems is introduced. We consider a class of elliptic problems which vary at a microscopic scale, and we aim at recovering the highly…

To accomplish correct Bayesian inference from weak lensing shear data requires a complete statistical description of the data. The natural framework to do this is a Bayesian Hierarchical Model, which divides the chain of reasoning into…

We present the starblade algorithm, a method to separate superimposed point sources from auto-correlated, diffuse flux using a Bayesian model. Point sources are assumed to be independent from each other and to follow a power-law brightness…

We present a Bayesian model calibration framework for inferring nonlinear constitutive relationships in heat conduction problems, with a focus on temperature-dependent thermal conductivity. The proposed framework integrates gradient-based…

We present a novel computational approach for extracting weak signals, whose exact location and width may be unknown, from complex background distributions with an arbitrary functional form. We focus on datasets that can be naturally…

This paper introduces a Bayesian framework to detect multiple signals embedded in noisy observations from a sensor array. For various states of knowledge on the communication channel and the noise at the receiving sensors, a marginalization…

The main contribution of this paper is to develop a hierarchical Bayesian formulation of PINNs for linear inverse problems, which is called BPINN-IP. The proposed methodology extends PINN to account for prior knowledge on the nature of the…

We consider filters for the detection and extraction of compact sources on a background. We make a one-dimensional treatment (though a generalization to two or more dimensions is possible) assuming that the sources have a Gaussian profile…

Bathymetry reconstruction is an important problem in various fields, including oceanography and environmental monitoring. This paper presents a Bayesian inference approach to reconstructing bathymetries from point measurements of the water…

A new type of dependent thinning for point processes in continuous space is proposed, which leverages the advantages of determinantal point processes defined on finite spaces and, as such, is particularly amenable to statistical, numerical,…

We derive an exact and efficient Bayesian regression algorithm for piecewise constant functions of unknown segment number, boundary location, and levels. It works for any noise and segment level prior, e.g. Cauchy which can handle outliers.…

We explore the possibility for using boundary data to identify sources in elliptic PDEs. Even though the associated forward operator has a large null space, it turns out that box constraints, combined with weighted sparsity regularization,…

We solve an inverse problem for the one-dimensional heat diffusion equation. We reconstruct the heat source function for the three types of data: 1) single position point and different times, 2) constant time and uniformly distributed…

Non-Gaussian Bayesian filtering is a core problem in stochastic filtering. The difficulty of the problem lies in parameterizing the state estimates. However the existing methods are not able to treat it well. We propose to use power moments…

After an artificial model background subtraction, the pixels have been labelled as foreground and background. Previous approaches to secondary processing the output for denoising usually use traditional methods such as the Bayesian…

Identification of local structure in intensive data -- such as time series, images, and higher dimensional processes -- is an important problem in astronomy. Since the data are typically generated by an inhomogeneous Poisson process, an…

We provide a complete framework for performing infinite-dimensional Bayesian inference and uncertainty quantification for image reconstruction with Poisson data. In particular, we address the following issues to make the Bayesian framework…

We develop a novel data-driven approach to the inverse problem of classical statistical mechanics: given experimental data on the collective motion of a classical many-body system, how does one characterise the free energy landscape of that…

We present a Bayesian methodology for infinite as well as finite dimensional parameter identification for partial differential equation models. The Bayesian framework provides a rigorous mathematical framework for incorporating prior…

Machine learning is now used in many areas of astrophysics, from detecting exoplanets in Kepler transit signals to removing telescope systematics. Recent work demonstrated the potential of using machine learning algorithms for atmospheric…