Related papers: Empirical Bayes Method for Large Scale Multiple Te…
While linear mixed modeling methods are foundational concepts introduced in any statistical education, adequate general methods for interval estimation involving models with more than a few variance components are lacking, especially in the…
The multivariate adaptive regression spline (MARS) approach of Friedman (1991) and its Bayesian counterpart (Francom et al. 2018) are effective approaches for the emulation of computer models. The traditional assumption of Gaussian errors…
Multivariate, heteroscedastic errors complicate statistical inference in many large-scale denoising problems. Empirical Bayes is attractive in such settings, but standard parametric approaches rest on assumptions about the form of the prior…
In prediction problems, it is common to model the data-generating process and then use a model-based procedure, such as a Bayesian predictive distribution, to quantify uncertainty about the next observation. However, if the posited model is…
This paper aims to develop an effective model-free inference procedure for high-dimensional data. We first reformulate the hypothesis testing problem via sufficient dimension reduction framework. With the aid of new reformulation, we…
{\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…
Motivated by the need to study the molecular mechanism underlying Type 1 Diabetes (T1D) with the gene expression data collected from both the patients and healthy controls at multiple time points, we propose an innovative method for jointly…
This paper proposes a unified framework to quantify local and global inferential uncertainty for high dimensional nonparanormal graphical models. In particular, we consider the problems of testing the presence of a single edge and…
Multiple hypothesis testing with false discovery rate (FDR) control is a fundamental problem in statistical inference, with broad applications in genomics, drug screening, and outlier detection. In many such settings, researchers may have…
We develop an empirical Bayes procedure for estimating the cell means in an unbalanced, two-way additive model with fixed effects. We employ a hierarchical model, which reflects exchangeability of the effects within treatment and within…
False discovery rate (FDR) is a cornerstone of modern multiple testing. However, it often fails to guarantee the reliability of "marginal" discoveries that lie at the boundary of the rejection set, which are often crucial in high-precision…
Traditional meta-analysis assumes that the effect sizes estimated in individual studies follow a Gaussian distribution. However, this distributional assumption is not always satisfied in practice, leading to potentially biased results. In…
Covariance matrix estimation is a fundamental statistical task in many applications, but the sample covariance matrix is sub-optimal when the sample size is comparable to or less than the number of features. Such high-dimensional settings…
Bayesian inference typically requires the computation of an approximation to the posterior distribution. An important requirement for an approximate Bayesian inference algorithm is to output high-accuracy posterior mean and uncertainty…
Multiple hypothesis testing is a fundamental problem in high dimensional inference, with wide applications in many scientific fields. In genome-wide association studies, tens of thousands of tests are performed simultaneously to find if any…
Testing composite null hypotheses arises in various applications, such as mediation and replicability analyses. The problem becomes more challenging in high-throughput experiments where tens of thousands of features are examined…
We propose a new empirical Bayes approach for inference in the $p \gg n$ normal linear model. The novelty is the use of data in the prior in two ways, for centering and regularization. Under suitable sparsity assumptions, we establish a…
Large-scale randomized experiments, sometimes called A/B tests, are increasingly prevalent in many industries. Though such experiments are often analyzed via frequentist $t$-tests, arguably such analyses are deficient: $p$-values are hard…
In this article, we propose a novel Bayesian multiple testing formulation for model and variable selection in inverse setups, judiciously embedding the idea of inverse reference distributions proposed by Bhattacharya (2013) in a mixture…
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…