Related papers: A General Framework for Empirical Bayes Estimation…

We propose a principled framework for nonparametric empirical Bayes (EB) estimation, based on the idea that the prior should be consistent with the observed posterior and that Bayesian updating should be stable. Focusing on discretized…

Bayesian learning has been recently considered as an effective means of accounting for uncertainty in trained deep network parameters. This is of crucial importance when dealing with small or sparse training datasets. On the other hand,…

Linear discriminant analysis (LDA) is a typical method for classification problems with large dimensions and small samples. There are various types of LDA methods that are based on the different types of estimators for the covariance…

In this paper a new family of minimum divergence estimators based on the Bregman divergence is proposed, where the defining convex function has an exponential nature. These estimators avoid the necessity of using an intermediate kernel…

In this work, we delve into the nonparametric empirical Bayes theory and approximate the classical Bayes estimator by a truncation of the generalized Laguerre series and then estimate its coefficients by minimizing the prior risk of the…

We propose an approximate hierarchical Bayes approach that uses the Natural Exponential Family with Quadratic Variance Function in combining information from multiple sources to improve traditional survey estimates of finite population…

The Bayesian predictive density has complex representation and does not belong to any finite-dimensional statistical model except for in limited situations. In this paper, we introduce its simple approximate representation employing its…

The empirical Bayes $g$-modeling approach via the nonparametric maximum likelihood estimator (NPMLE) is widely used for large-scale estimation and inference in the normal means problem, yet theoretical guarantees for uncertainty…

The ability to reconstruct high-quality images from undersampled MRI data is vital in improving MRI temporal resolution and reducing acquisition times. Deep learning methods have been proposed for this task, but the lack of verified methods…

We study a general factor analysis framework where the $n$-by-$p$ data matrix is assumed to follow a general exponential family distribution entry-wise. While this model framework has been proposed before, we here further relax its…

The Robbins estimator is the most iconic and widely used procedure in the empirical Bayes literature for the Poisson model. On one hand, this method has been recently shown to be minimax optimal in terms of the regret (excess risk over the…

One of the most common analysis tasks in genomic research is to identify genes that are differentially expressed (DE) between experimental conditions. Empirical Bayes (EB) statistical tests using moderated genewise variances have been very…

Random effects model can account for the lack of fitting a regression model and increase precision of estimating area-level means. However, in case that the synthetic mean provides accurate estimates, the prior distribution may inflate an…

We describe different Bayesian ensemble refinement methods, examine their interrelation, and discuss their practical application. With ensemble refinement, the properties of dynamic and partially disordered (bio)molecular structures can be…

Harvey et al. (2010) extended the Bayesian estimation method by Sahu et al. (2003) to a multivariate skew-elliptical distribution with a general skewness matrix, and applied it to Bayesian portfolio optimization with higher moments.…

We present Nested Sampling with Slice-within-Gibbs (NS-SwiG), an algorithm for Bayesian inference and evidence estimation in high-dimensional models whose likelihood admits a factorization, such as hierarchical Bayesian models. We construct…

Gaussian empirical Bayes methods usually maintain a precision independence assumption: The unknown parameters of interest are independent from the known standard errors of the estimates. This assumption is often theoretically questionable…

{\bf Abstract} Consider a Non-Parametric Empirical Bayes (NPEB) setup. We observe $Y_i, \sim f(y|\theta_i)$, $\theta_i \in \Theta$ independent, where $\theta_i \sim G$ are independent $i=1,...,n$. The mixing distribution $G$ is unknown $G…

We consider a Nonparametric Empirical Bayes (NPEB) framework. Let $Y_i$ be random variables, $Y_i \sim f(y|\theta_i)$, $i=1,...,n$, where $\theta_i \sim G$, and $\theta_i \in \Theta$ are independent. The variables $Y_i $ are conditionally…

In this paper, we consider objective Bayesian inference of the generalized exponential distribution using the independence Jeffreys prior and validate the propriety of the posterior distribution under a family of structured priors. We…