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This paper considers the problem of recovering a structured signal from a relatively small number of noisy measurements with the aid of a similar signal which is known beforehand. We propose a new approach to integrate prior information…
This work presents a novel and effective method for fitting multidimensional ellipsoids to scattered data in the contamination of noise and outliers. We approach the problem as a Bayesian parameter estimate process and maximize the…
Sampling from the posterior is a key technical problem in Bayesian statistics. Rigorous guarantees are difficult to obtain for Markov Chain Monte Carlo algorithms of common use. In this paper, we study an alternative class of algorithms…
Sensor noise sources cause differences in the signal recorded across pixels in a single image and across multiple images. This paper presents a Bayesian approach to decomposing and characterizing the sensor noise sources involved in imaging…
Bayesian inference allows machine learning models to express uncertainty. Current machine learning models use only a single learnable parameter combination when making predictions, and as a result are highly overconfident when their…
Recovering a signal from its degraded measurements is a long standing challenge in science and engineering. Recently, zero-shot diffusion based methods have been proposed for such inverse problems, offering a posterior sampling based…
We present a Bayesian data fusion method to approximate a posterior distribution from an ensemble of particle estimates that only have access to subsets of the data. Our approach relies on approximate probabilistic inference of model…
In the Bayesian approach, the a priori knowledge about the input of a mathematical model is described via a probability measure. The joint distribution of the unknown input and the data is then conditioned, using Bayes' formula, giving rise…
In particle physics, as in many areas of science, parameter inference relies on simulations to bridge the gap between theory and experiment. Recent developments in simulation-based inference have boosted the sensitivity of analyses;…
Inverse problems can be described as limited-data problems in which the signal of interest cannot be observed directly. A physics-based forward model that relates the signal with the observations is typically needed. Unfortunately, unknown…
This paper is concerned with the numerical solution of model-based, Bayesian inverse problems. We are particularly interested in cases where the cost of each likelihood evaluation (forward-model call) is expensive and the number of un-…
Bayesian models provide recursive inference naturally because they can formally reconcile new data and existing scientific information. However, popular use of Bayesian methods often avoids priors that are based on exact posterior…
Motivated by single-particle cryo-electron microscopy, multi-reference alignment (MRA) models the task of recovering an unknown signal from multiple noisy observations corrupted by random rotations. The standard approach,…
Importance sampling is a popular technique in Bayesian inference: by reweighting samples drawn from a proposal distribution we are able to obtain samples and moment estimates from a Bayesian posterior over latent variables. Recent work,…
We propose two novel approaches to the recovery of an (approximately) sparse signal from noisy linear measurements in the case that the signal is a priori known to be non-negative and obey given linear equality constraints, such as simplex…
Bayesian inference for inverse problems hinges critically on the choice of priors. In the absence of specific prior information, population-level distributions can serve as effective priors for parameters of interest. With the advent of…
Posterior sampling by Monte Carlo methods provides a more comprehensive solution approach to inverse problems than computing point estimates such as the maximum posterior using optimization methods, at the expense of usually requiring many…
We study super-resolution multi-reference alignment, the problem of estimating a signal from many circularly shifted, down-sampled, and noisy observations. We focus on the low SNR regime, and show that a signal in $\mathbb{R}^M$ is uniquely…
The typical approach for recovery of spatially correlated signals is regularized least squares with a coupled regularization term. In the Bayesian framework, this algorithm is seen as a maximum-a-posterior estimator whose postulated prior…
Many recently developed Bayesian methods have focused on sparse signal detection. However, much less work has been done addressing the natural follow-up question: how to make valid inferences for the magnitude of those signals after…