Related papers: General empirical Bayes wavelet methods and exactl…

Estimation of the allele frequency at genetic markers is a key ingredient in biological and biomedical research, such as studies of human genetic variation or of the genetic etiology of heritable traits. As genetic data becomes increasingly…

We consider a problem of statistical mean estimation in which the samples are not observed directly, but are instead observed by a relay (``teacher'') that transmits information through a memoryless channel to the decoder (``student''), who…

For continuous-time linear stochastic dynamical systems driven by Wiener processes, we consider the problem of designing ensemble filters when the observation process is randomly time-sampled. We propose a continuous-discrete McKean--Vlasov…

Many statistical problems involve data from thousands of parallel cases. Each case has some associated effect size, and most cases will have no effect. It is often important to estimate the effect size and the local or tail-area false…

We propose a fast and theoretically grounded method for Bayesian variable selection and model averaging in latent variable regression models. Our framework addresses three interrelated challenges: (i) intractable marginal likelihoods, (ii)…

Empirical Bayes methods are widely used for large-scale estimation and inference in the Poisson means problem. Existing results establish theoretical properties of the nonparametric maximum likelihood estimator (NPMLE) for optimal posterior…

The generalized approximate message passing (GAMP) algorithm under the Bayesian setting shows advantage in recovering under-sampled sparse signals from corrupted observations. Compared to conventional convex optimization methods, it has a…

The simplest, and most common, stochastic model for population processes, including those from biochemistry and cell biology, are continuous time Markov chains. Simulation of such models is often relatively straightforward as there are…

In this article, a general problem of sequential statistical inference for general discrete-time stochastic processes is considered. The problem is to minimize an average sample number given that Bayesian risk due to incorrect decision does…

A dynamical model consists of a continuous self-map $T: \mathcal{X} \to \mathcal{X}$ of a compact state space $\mathcal{X}$ and a continuous observation function $f: \mathcal{X} \to \mathbb{R}$. This paper considers the fitting of a…

We consider the problem of estimating the unknown response function in the multichannel deconvolution model with long-range dependent Gaussian errors. We do not limit our consideration to a specific type of long-range dependence rather we…

Inspired by the key principle behind the EM algorithm, we propose a general methodology for conducting wavelet estimation with irregularly-spaced data by viewing the data as the observed portion of an augmented regularly-spaced data set. We…

We introduce a flexible empirical Bayes approach for fitting Bayesian generalized linear models. Specifically, we adopt a novel mean-field variational inference (VI) method and the prior is estimated within the VI algorithm, making the…

This paper offers a qualitative insight into the convergence of Bayesian parameter inference in a setup which mimics the modeling of the spread of a disease with associated disease measurements. Specifically, we are interested in the…

We propose a method to improve the efficiency and accuracy of amortized Bayesian inference by leveraging universal symmetries in the joint probabilistic model of parameters and data. In a nutshell, we invert Bayes' theorem and estimate the…

In this paper we propose a semi-parametric Bayesian Generalized Least Squares estimator. In a generic setting where each error is a vector, the parametric Generalized Least Square estimator maintains the assumption that each error vector…

We consider the problem of statistical inference on parameters of a target population when auxiliary observations are available from related populations. We propose a flexible empirical Bayes approach that can be applied on top of any…

Large-sample Bayesian analogs exist for many frequentist methods, but are less well-known for the widely-used 'sandwich' or 'robust' variance estimates. We review existing approaches to Bayesian analogs of sandwich variance estimates and…

The empirical risk minimization approach to data-driven decision making requires access to training data drawn under the same conditions as those that will be faced when the decision rule is deployed. However, in a number of settings, we…

Empirical Bayes methods have been around for a long time and have a wide range of applications. These methods provide a way in which historical data can be aggregated to provide estimates of the posterior mean. This thesis revisits some of…