Related papers: Multiscale Shrinkage and L\'evy Processes
The negative multinomial distribution is a multivariate generalization of the negative binomial distribution. In this paper, we consider the problem of estimating an unknown matrix of probabilities on the basis of observations of negative…
We propose a flexible class of models based on scale mixture of uniform distributions to construct shrinkage priors for covariance matrix estimation. This new class of priors enjoys a number of advantages over the traditional scale mixture…
Shrinkage prior are becoming more and more popular in Bayesian modeling for high dimensional sparse problems due to its computational efficiency. Recent works show that a polynomially decaying prior leads to satisfactory posterior…
Symbolic regression is a powerful tool for discovering governing equations directly from data, but its sensitivity to noise hinders its broader application. This paper introduces a Sequential Monte Carlo (SMC) framework for Bayesian…
Bayesian methods have proved powerful in many applications for the inference of model parameters from data. These methods are based on Bayes' theorem, which itself is deceptively simple. However, in practice the computations required are…
We study Bayesian inverse problems with mixed noise, modeled as a combination of additive and multiplicative Gaussian components. While traditional inference methods often assume fixed or known noise characteristics, real-world…
The present work describes simulation studies to compare the performances of bayesian wavelet shrinkage methods in estimating component curves from aggregated functional data. To do so, five methods were considered: the bayesian shrinkage…
In this article we consider parametric Bayesian inference for stochastic differential equations (SDE) driven by a pure-jump stable Levy process, which is observed at high frequency. In most cases of practical interest, the likelihood…
Local clock models propose that the rate of molecular evolution is constant within phylogenetic sub-trees. Current local clock inference procedures scale poorly to large taxa problems, impose model misspecification, or require a priori…
The trend in modern science and technology is to take vector measurements rather than scalars, ruthlessly scaling to ever higher dimensional vectors. For about two decades now, traditional scalar Compressed Sensing has been synonymous with…
We consider a Bayesian framework for estimating a high-dimensional sparse precision matrix, in which adaptive shrinkage and sparsity are induced by a mixture of Laplace priors. Besides discussing our formulation from the Bayesian…
Many probabilistic models of interest in scientific computing and machine learning have expensive, black-box likelihoods that prevent the application of standard techniques for Bayesian inference, such as MCMC, which would require access to…
We propose a flexible Bayesian approach for sparse Gaussian graphical modeling of multivariate time series. We account for temporal correlation in the data by assuming that observations are characterized by an underlying and unobserved…
We investigate the posterior rate of convergence for wavelet shrinkage using a Bayesian approach in general Besov spaces. Instead of studying the Bayesian estimator related to a particular loss function, we focus on the posterior…
In this paper, we propose a scalable Bayesian method for sparse covariance matrix estimation by incorporating a continuous shrinkage prior with a screening procedure. In the first step of the procedure, the off-diagonal elements with small…
We propose a shrinkage procedure for simultaneous variable selection and estimation in generalized linear models (GLMs) with an explicit predictive motivation. The procedure estimates the coefficients by minimizing the Kullback-Leibler…
We study data-driven decision-making problems in the Bayesian framework, where the expectation in the Bayes risk is replaced by a risk-sensitive entropic risk measure. We focus on problems where calculating the posterior distribution is…
We consider a new statistical model called the circulant correlation structure model, which is a multivariate Gaussian model with unknown covariance matrix and has a scale-invariance property. We construct shrinkage priors for the circulant…
This paper advocates proximal Markov Chain Monte Carlo (ProxMCMC) as a flexible and general Bayesian inference framework for constrained or regularized estimation. Originally introduced in the Bayesian imaging literature, ProxMCMC employs…
This paper focuses on Bayesian shrinkage for covariance matrix estimation. We examine posterior properties and frequentist risks of Bayesian estimators based on new hierarchical inverse-Wishart priors. More precisely, we give the existence…