Related papers: Moment-based Posterior Sampling for Multi-referenc…
For a Bayesian, real-time forecasting with the posterior predictive distribution can be challenging for a variety of time series models. First, estimating the parameters of a time series model can be difficult with sample-based approaches…
Solving inverse problems involving measurement noise and modeling errors requires regularization in order to avoid data overfit. Geophysical inverse problems, in which the Earth's highly heterogeneous structure is unknown, present a…
Motivated by modern data applications such as cryo-electron microscopy, the goal of classic multi-reference alignment (MRA) is to recover an unknown signal $f: \mathbb{R} \to \mathbb{R}$ from many observations that have been randomly…
We consider the inverse problem of estimating an unknown function $u$ from noisy measurements $y$ of a known, possibly nonlinear, map $\mathcal{G}$ applied to $u$. We adopt a Bayesian approach to the problem and work in a setting where the…
Geophysical inverse problems are often ill-posed and admit multiple solutions. Conventional discriminative methods typically yield a single deterministic solution, which fails to model the posterior distribution, cannot generate diverse…
We consider inverse problems in Hilbert spaces under correlated Gaussian noise and use a Bayesian approach to find their regularised solution. We focus on mildly ill-posed inverse problems with the noise being generalised derivative of…
We propose a novel adaptive importance sampling scheme for Bayesian inversion problems where the inference of the variables of interest and the power of the data noise is split. More specifically, we consider a Bayesian analysis for the…
We consider the problem of estimating a variable number of parameters with a dynamic nature. A familiar example is finding the position of moving targets using sensor array observations. The problem is challenging in cases where either the…
Most applications of Bayesian Inference for parameter estimation and model selection in astrophysics involve the use of Monte Carlo techniques such as Markov Chain Monte Carlo (MCMC) and nested sampling. However, these techniques are time…
We present a novel Bayesian model and a corresponding robust, probabilistic calibration procedure for the CORSAIR polarimeter that can be applied to other polarimeters. Our calibration procedure combines existing Mueller matrix…
In this article, we propose a novel method for sampling potential functions based on noisy observation data of a finite number of observables in quantum canonical ensembles, which leads to the accurate sampling of a wide class of test…
Reconstructing astrophysical and cosmological fields from observations is challenging. It requires accounting for non-linear transformations, mixing of spatial structure, and noise. In contrast, forward simulators that map fields to…
We propose a recursive Bayesian estimation procedure for multivariate autoregressive models with exogenous inputs based on message passing in a factor graph. Unlike recursive least-squares, our method produces full posterior distributions…
We consider a class of linear ill-posed inverse problems arising from inversion of a compact operator with singular values which decay exponentially to zero. We adopt a Bayesian approach, assuming a Gaussian prior on the unknown function.…
This paper presents a study of the large-sample behavior of the posterior distribution of a structural parameter which is partially identified by moment inequalities. The posterior density is derived based on the limited information…
Motivated by cutting-edge applications like cryo-electron microscopy (cryo-EM), the Multi-Reference Alignment (MRA) model entails the learning of an unknown signal from repeated measurements of its images under the latent action of a group…
We consider the problem of estimating cross-spectral quantities in the low-frequency regime, where long observation times limit averaging over large ensembles of periodograms, thereby preventing the use of approximate Gaussian statistics.…
Model-assisted estimation with complex survey data is an important practical problem in survey sampling. When there are many auxiliary variables, selecting significant variables associated with the study variable would be necessary to…
In this paper, we propose a Bayesian MAP estimator for solving the deconvolution problems when the observations are corrupted by Poisson noise. Towards this goal, a proper data fidelity term (log-likelihood) is introduced to reflect the…
Efficiently sampling from high-dimensional, multi-modal posteriors is a central challenge in Bayesian inference for astrophysics, especially gravitational-wave astronomy. Popular families of methods like Markov-chain Monte Carlo, nested…