Related papers: Perfect simulation for Bayesian wavelet thresholdi…

We study the problem of estimating the mode and maximum of an unknown regression function in the presence of noise. We adopt the Bayesian approach by using tensor-product B-splines and endowing the coefficients with Gaussian priors. In the…

We derive a formula for optimal hard thresholding of the singular value decomposition in the presence of correlated additive noise; although it nominally involves unobservables, we show how to apply it even where the noise covariance…

Experimentally observed networks of interacting dynamical systems are inferred from recorded multivariate time series by evaluating a statistical measure of dependence, usually the cross-correlation coefficient, or mutual information. These…

Discrete Markov random fields are undirected graphical models that capture complex conditional dependencies between discrete variables. Conducting exact posterior inference in these models is often computationally challenging because…

In many applications, flow measurements are usually sparse and possibly noisy. The reconstruction of a high-resolution flow field from limited and imperfect flow information is significant yet challenging. In this work, we propose an…

We consider the asymptotic behavior of posterior distributions and Bayes estimators based on observations which are required to be neither independent nor identically distributed. We give general results on the rate of convergence of the…

In this paper we present a blind deconvolution scheme based on statistical wavelet estimation. We assume no prior knowledge of the wavelet, and do not select a reflector from the signal. Instead, the wavelet (ultrasound pulse) is…

Sparse signal reconstruction algorithms have attracted research attention due to their wide applications in various fields. In this paper, we present a simple Bayesian approach that utilizes the sparsity constraint and a priori statistical…

Gaussian graphical models typically assume a homogeneous structure across all subjects, which is often restrictive in applications. In this article, we propose a weighted pseudo-likelihood approach for graphical modeling which allows…

Inverse problems constrained by partial differential equations are often ill-conditioned due to noisy and incomplete data or inherent non-uniqueness. A prominent example is full waveform inversion, which estimates Earth's subsurface…

Compressed sensing allows perfect recovery of sparse signals (or signals sparse in some basis) using only a small number of random measurements. Existing results in compressed sensing literature have focused on characterizing the achievable…

We introduce a new approach for decoupling trends (drift) and changepoints (shifts) in time series. Our locally adaptive model-based approach for robustly decoupling combines Bayesian trend filtering and machine learning based…

We consider the problem of reconstructing wideband frequency spectra from distributed, compressive measurements. The measurements are made by a network of nodes, each independently mixing the ambient spectra with low frequency, random…

We study a nonparametric Bayesian approach to linear inverse problems under discrete observations. We use the discrete Fourier transform to convert our model into a truncated Gaussian sequence model, that is closely related to the classical…

We apply Bayesian statistics to the estimation of correlation functions. We give the probability distributions of auto- and cross-correlations as functions of the data. Our procedure uses the measured data optimally and informs about the…

A large empirical literature regresses outcomes on empirical Bayes shrinkage estimates of value-added, yet little is known about whether this approach leads to unbiased estimates and valid inference for the downstream regression…

We consider the Bayesian detection statistic for a targeted search for continuous gravitational waves, known as the $\mathcal{B}$-statistic. This is a Bayes factor between signal and noise hypotheses, produced by marginalizing over the four…

Sampling in shift-invariant spaces is a realistic model for signals with smooth spectrum. In this paper, we consider phaseless sampling and reconstruction of real-valued signals in a shift-invariant space from their magnitude measurements…

This paper deals with the problem of the multivariate copula density estimation. Using wavelet methods we provide two shrinkage procedures based on thresholding rules for which the knowledge of the regularity of the copula density to be…

Cosmological experiments often employ Bayesian workflows to derive constraints on cosmological and astrophysical parameters from their data. It has been shown that these constraints can be combined across different probes such as Planck and…