Related papers: Bayesian Estimators for Small Area Models Shrinkin…
We propose a procedure to handle the problem of Gaussian regression when the variance is unknown. We mix least-squares estimators from various models according to a procedure inspired by that of Leung and Barron (2007). We show that in some…
During the past decade, shrinkage priors have received much attention in Bayesian analysis of high-dimensional data. This paper establishes the posterior consistency for high-dimensional linear regression with a class of shrinkage priors,…
We wish to compute the gradient of an expectation over a finite or countably infinite sample space having $K \leq \infty$ categories. When $K$ is indeed infinite, or finite but very large, the relevant summation is intractable. Accordingly,…
This paper presents a simple shrinkage estimator of rates based on Bayesian methods. Our focus is on crime rates as a motivating example. The estimator shrinks each town's observed crime rate toward the country-wide average crime rate…
Computer experiments are becoming increasingly important in scientific investigations. In the presence of uncertainty, analysts employ probabilistic sensitivity methods to identify the key-drivers of change in the quantities of interest.…
Hierarchical models represent a challenging setting for inference algorithms. MCMC methods struggle to scale to large models with many local variables and observations, and variational inference (VI) may fail to provide accurate…
This paper develops a novel approach to random effects estimation and individual-level forecasting in micropanels, targeting individual accuracy rather than aggregate performance. The conventional shrinkage methods used in the literature,…
We study the distribution of hard-, soft-, and adaptive soft-thresholding estimators within a linear regression model where the number of parameters k can depend on sample size n and may diverge with n. In addition to the case of known…
We consider sparse Bayesian estimation in the classical multivariate linear regression model with $p$ regressors and $q$ response variables. In univariate Bayesian linear regression with a single response $y$, shrinkage priors which can be…
In statistical exercises where there are several candidate models, the traditional approach is to select one model using some data driven criterion and use that model for estimation, testing and other purposes, ignoring the variability of…
This paper considers the problem of computing Bayesian estimates of both states and model parameters for nonlinear state-space models. Generally, this problem does not have a tractable solution and approximations must be utilised. In this…
We tackle the problem of the estimation of a vector of means from a single vector-valued observation $y$. Whereas previous work reduces the size of the estimates for the largest (absolute) sample elements via shrinkage (like James-Stein) or…
Environmental processes resolved at a sufficiently small scale in space and time will inevitably display non-stationary behavior. Such processes are both challenging to model and computationally expensive when the data size is large.…
Evaluating treatment effect heterogeneity across patient subgroups is a fundamental aspect of clinical trial analysis. Yet, these analyses have inherent limitations due to small sample sizes and the substantial number of subgroups…
Bayesian analysis is a framework for parameter estimation that applies even in uncertainty regimes where the commonly used local (frequentist) analysis based on the Cram\'er-Rao bound is not well defined. In particular, it applies when no…
We develop a Bayesian methodology aimed at simultaneously estimating low-rank and row-sparse matrices in a high-dimensional multiple-response linear regression model. We consider a carefully devised shrinkage prior on the matrix of…
This paper introduces a novel Bayesian approach to detect changes in the variance of a Gaussian sequence model, focusing on quantifying the uncertainty in the change point locations and providing a scalable algorithm for inference. Such a…
Ranking, and inferences based on ranking of a set of entities, are important problems in numerous contexts. This is especially true in small area statistics where there may be only a limited amount of directly observed data from each entity…
We develop and evaluate point and interval estimates for the random effects $\theta_i$, having made observations $y_i|\theta_i\stackrel{\m athit{ind}}{\sim}N[\theta_i,V_i],i=1,...,k$ that follow a two-level Normal hierarchical model.…
The estimation of the mean matrix of the multivariate normal distribution is addressed in the high dimensional setting. Efron-Morris-type linear shrinkage estimators based on ridge estimators for the precision matrix instead of the…