This paper deals with the problem of selecting good negative binomial populations as compared with a standard or a control. The main results are based on the use of the empirical Bayes approach. First we derive the monotone empirical Bayes estimators of the concerned parameters. Based on these estimators, we construct monotone empirical Bayes selection rules. Asymptotic optimality properties of...

For the problem of variable selection for the normal linear model, fixed penalty selection criteria such as AIC, Cp, BIC and RIC correspond to the posterior modes of a hierarchical Bayes model for various fixed hyperparameter settings. Adaptive selection criteria obtained by empirical Bayes estimation of the hyperparameters have been shown by George and Foster [2000. Calibration and Empirical B...

Consider an experiment yielding an observable random quantity X whose distribution Fθ depends on a parameter θ with θ being distributed according to some distribution G0. We study the Bayesian estimation problem of θ under squared error loss function based on X, as well as some additional data available from other similar experiments according to an empirical Bayes structure. In a recent paper,...

We generalize the approach of Liu and Lawrence (1999) for multiple changepoint problems where the number of changepoints is unknown. The approach is based on dynamic programming recursion for efficient calculation of the marginal probability of the data with the hidden parameters integrated out. For the estimation of the hyperparameters, we propose to use Monte Carlo EM when training data are a...

Abstract We review the empirical Bayes approach to large-scale inference. In context of problem inference for a high-dimensional normal mean, methods are advocated as they exhibit risk-reducing shrinkage, while establishing appropriate control frequentist properties elucidate these and evaluate protection that provides against selection bias.

We construct robust empirical Bayes confidence intervals (EBCIs) in a normal means problem. The are centered at the usual linear estimator, but use critical value accounting for shrinkage. Parametric EBCIs that assume distribution (Morris, 1983b) may substantially undercover when this assumption is violated. In contrast, our control coverage regardless of distribution, while remaining close len...