Related papers: Empirical Bayes for the Reluctant Frequentist
Bayesian and frequentist methods differ in many aspects, but share some basic optimality properties. In practice, there are situations in which one of the methods is more preferred by some criteria. We consider the case of inference about a…
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…
Empirical Bayes is a versatile approach to `learn from a lot' in two ways: first, from a large number of variables and second, from a potentially large amount of prior information, e.g. stored in public repositories. We review applications…
When dealing with Bayesian inference the choice of the prior often remains a debatable question. Empirical Bayes methods offer a data-driven solution to this problem by estimating the prior itself from an ensemble of data. In the…
The simultaneous estimation of multiple unknown parameters lies at heart of a broad class of important problems across science and technology. Currently, the state-of-the-art performance in the such problems is achieved by nonparametric…
Bayesian inference is attractive for its coherence and good frequentist properties. However, it is a common experience that eliciting a honest prior may be difficult and, in practice, people often take an {\em empirical Bayes} approach,…
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…
This study examines the application of Bayesian approach in the context of clinical trials, emphasizing their increasing importance in contemporary biomedical research. While conventional frequentist approach provides a foundational basis…
Due to their great flexibility, nonparametric Bayes methods have proven to be a valuable tool for discovering complicated patterns in data. The term "nonparametric Bayes" suggests that these methods inherit model-free operating…
We propose a robust Bayesian method for economic models that can be rejected by some data distributions. The econometrician starts with a refutable structural assumption which can be written as the intersection of several assumptions. To…
As the frontiers of applied statistics progress through increasingly complex experiments we must exploit increasingly sophisticated inferential models to analyze the observations we make. In order to avoid misleading or outright erroneous…
The problem of nonparametric estimation of the conditional density of a response, given a vector of explanatory variables, is classical and of prominent importance in many prediction problems since the conditional density provides a more…
Empirical Bayes methods use the data from parallel experiments, for instance, observations $X_k\sim\mathcal{N}(\Theta_k,1)$ for $k=1,2,\ldots,N$, to estimate the conditional distributions $\Theta_k|X_k$. There are two main estimation…
Count outcomes in longitudinal studies are frequent in clinical and engineering studies. In frequentist and Bayesian statistical analysis, methods such as Mixed linear models allow the variability or correlation within individuals to be…
Bayes Factors, the Bayesian tool for hypothesis testing, are receiving increasing attention in the literature. Compared to their frequentist rivals ($p$-values or test statistics), Bayes Factors have the conceptual advantage of providing…
An empirical Bayes problem has an unknown prior to be estimated from data. The predictive recursion (PR) algorithm provides fast nonparametric estimation of mixing distributions and is ideally suited for empirical Bayes applications. This…
We propose a flexible and identifiable version of the two-groups model, motivated by hierarchical Bayes considerations, that features an empirical null and a semiparametric mixture model for the non-null cases. We use a computationally…
In this study, we consider an empirical Bayes method for Boltzmann machines and propose an algorithm for it. The empirical Bayes method allows estimation of the values of the hyperparameters of the Boltzmann machine by maximizing a specific…
A new empirical Bayes approach to variable selection in the context of generalized linear models is developed. The proposed algorithm scales to situations in which the number of putative explanatory variables is very large, possibly much…
One of the main goals of mathematical modeling in systems medicine related to medical applications is to obtain patient-specific parameterizations and model predictions. In clinical practice, however, the number of available measurements…