We suppose that the statistician observes some large number of estimates z(i), each with its own unobserved expectation parameter μ(i). The largest few of the z(i)'s are likely to substantially overestimate their corresponding μ(i)'s, this being an example of selection bias, or regression to the mean. Tweedie's formula, first reported by Robbins in 1956, offers a simple empirical Bayes approach...

We propose model-based inference for differential gene expression, using a non-parametric Bayesian probability model for the distribution of gene intensities under different conditions. The probability model is essentially a mixture of normals. The resulting inference is similar to the empirical Bayes approach proposed in Efron et al. (2001). The use of fully modelbased inference mitigates some...

In this paper, the naive credal classifier, which is a set-valued counterpart of naive Bayes, is extended to a general and flexible treatment of incomplete data, yielding a new classifier called naive credal classifier 2 (NCC2). The new classifier delivers classifications that are reliable even in the presence of small sample sizes and missing values. Extensive empirical evaluations show that, ...

The author proposes to use weighted likelihood to approximate Bayesian inference when no external or prior information is available. He proposes a weighted likelihood estimator that minimizes the empirical Bayes risk under relative entropy loss. He discusses connections among the weighted likelihood, empirical Bayes and James–Stein estimators. Both simulated and real data sets are used for illu...

1 This study evaluates the safety effects of automated mobile enforcement on urban arterial roads. 2 The before-and-after Empirical Bayes (EB) method was used to account for the regression-to3 the-mean effects and other confounding factors. Locally developed safety performance functions 4 and yearly calibration factors for different collision severities were obtained by using a reference 5 grou...

Current molecular methods of species delimitation are limited by the types of species delimitation models and scenarios that can be tested. Bayes factors allow for more flexibility in testing non-nested species delimitation models and hypotheses of individual assignment to alternative lineages. Here, we examined the efficacy of Bayes factors in delimiting species through simulations and empiric...

STATISTICAL ANALYSIS IN EMPIRICAL BAYES AND IN CAUSAL INFERENCE

It is well known that in unidentifiable models, the Bayes estimation has the advantage of generalization performance to the maximum likelihood estimation. However, accurate approximation of the posterior distribution requires huge computational costs. In this paper, we consider an empirical Bayes approach where a part of the parameters are regarded as hyperparameters, which we call a subspace B...