empirical bayes stabilization

This study addresses the challenge of specifying prior parameters for both fixed and random effects in linear mixed models when dealing with high-dimensional data or complex covariance structures. The authors propose a data-driven joint shrinkage approach that, within an empirical Bayes framework, employs Laplace approximation to efficiently maximize the marginal likelihood and automatically select prior parameters for both effect types. This method represents the first to jointly and adaptively estimate priors for fixed and random effects, overcoming the limitations of conventional approaches that rely on manual specification. Numerical experiments demonstrate that the proposed method significantly outperforms existing techniques in terms of parameter estimation accuracy and predictive performance. Its effectiveness in modeling complex random-effect structures is further validated through application to real-world data on air pollution and health outcomes.

This study addresses the “winner’s curse” in A/B testing, where selection effects induce upward bias in treatment effect estimates and invalidate confidence intervals—particularly under low statistical power, thereby compromising decision-making. To mitigate this, the authors propose the Bayesian Hierarchical Shrinkage (BHS) method, which operates within an empirical Bayes framework and introduces experiment-specific local shrinkage factors. By constructing data-driven priors that incorporate individual experiment characteristics, BHS effectively corrects for selection bias while enhancing robustness to prior misspecification, overcoming the limitations of traditional approaches that apply uniform shrinkage. The method admits closed-form inference, making it suitable for high-throughput production environments. Empirical evaluations on both simulated and real-world Meta data demonstrate that BHS substantially reduces estimation bias and achieves more accurate interval coverage, even under severe model misspecification.

This work addresses the sensitivity of empirical Bayes denoising in Gaussian sequence models to prior specification and the assumption of Gaussian noise. To enhance robustness against model misspecification, the authors integrate the Hodges–Lehmann constrained Bayes framework with Huber–Mallows robust statistical principles. The proposed method mitigates reliance on both the initial prior and the Gaussianity of the noise by explicitly limiting the influence of the prior and relaxing the strict Gaussian noise assumption. Experimental results demonstrate that the approach significantly improves estimation stability and adaptability under realistic data perturbations, thereby enhancing the practical utility of empirical Bayes denoising in non-ideal settings.

This paper addresses the bias and invalid inference arising when empirical Bayes shrinkage estimators—such as teacher value-added measures—are used as regressors in downstream linear regression. We systematically analyze the asymptotic bias induced by ignoring heteroskedastic noise structure in the shrinkage estimates. We prove theoretically that ordinary least squares (OLS) regression on the shrinkage estimates automatically corrects for this bias: the resulting coefficient estimators are asymptotically unbiased, normal, and efficient—statistically equivalent to those obtained using the true (unobserved) latent variables. Crucially, this result holds without requiring explicit heteroskedasticity modeling or ad hoc adjustments; standard OLS standard errors suffice for valid, efficient inference. Our contribution is the first rigorous justification of “plug-in” regression using shrinkage estimators, establishing its formal validity under heteroskedasticity. This provides a simple, robust, and theoretically grounded framework for causal inference in empirical settings including educational evaluation and performance measurement.

Existing random-effects estimators—such as James–Stein and empirical Bayes—optimize overall (population-level) risk, often at the expense of individual prediction accuracy. This paper addresses micro-panel data and proposes an Individual Weighting (IW) shrinkage estimator: it replaces conventional cross-sectional information with each unit’s own time-series history for shrinkage, thereby overcoming the “majority-dominates” limitation inherent in standard approaches. IW constructs feasible weights guided by the minimax regret criterion, ensuring individual-risk optimality under weaker assumptions than traditional methods. Theoretically, the IW estimator achieves asymptotic individual-level optimality and substantially reduces systematic bias. Empirically, it delivers superior individual-level predictive accuracy compared to leading alternatives. Crucially, this work is the first to endogenize temporal structure directly into the shrinkage mechanism—yielding a more interpretable and practically useful framework for micro-level decision-making.

This work addresses Bayesian shrinkage estimation for the mean of a multivariate normal distribution under multiple prior target information. It proposes a general construction that, for the first time, explicitly yields a proper Bayes minimax multiple-shrinkage estimator. The method leverages a mixture structure based on square-root-harmonic marginal densities to adaptively shrink toward the more favorable among several prespecified targets, thereby overcoming limitations of existing approaches that rely on either a single target or improper priors. The resulting estimator possesses minimaxity, uniformly dominating the maximum likelihood estimator in terms of risk and achieving substantial risk reduction over a broad region of the parameter space, thus enhancing both robustness and efficiency.

研究通过使用Empirical Bayies方法中的g-modeling策略有效解决了在复合自适应实验中估计未知均值的问题，即使数据非外生收集也能保证有效性。

This study addresses the high variance and instability in subgroup treatment effect estimation commonly encountered in clinical trials due to small sample sizes and numerous subgroups. The authors propose a unified Bayesian shrinkage framework that accommodates continuous, binary, count, and time-to-event endpoints, integrating both univariate and global modeling strategies. By employing hierarchical priors that shrink subgroup-specific effects toward the overall treatment effect, the approach enhances estimation robustness. For the first time, multiple Bayesian shrinkage methods are systematically implemented in the open-source R package `bonsaiforest2`, with comprehensive performance evaluations across diverse endpoint types and simulation scenarios. Results demonstrate that shrinkage estimators substantially reduce mean squared error and more effectively identify non-beneficial subgroups. The global model consistently outperforms alternatives and exhibits greater robustness to hyperprior specifications, supporting its routine use in forest plots to inform clinical decision-making.

This study reevaluates the efficacy of empirical Bayes methods for parameter estimation in binomial (with Beta priors) and Poisson models. Through theoretical analysis and extensive numerical experiments, it specifically investigates Type-II maximum likelihood (ML-II) under general two-parameter Beta priors and extends the examination to the Gamma–Poisson setting. The findings reveal that the ML-II procedure fails under a general two-parameter Beta prior; even when restricted to a symmetric one-parameter Beta prior, the resulting estimator does not substantially outperform the maximum likelihood estimator under quadratic loss. These results challenge the commonly presumed superiority of empirical Bayes approaches in point estimation and provide a critical counterexample grounded in rigorous empirical evidence.

This study addresses the challenges of calibrating Bayesian hierarchical priors and the computational inefficiency of posterior inference in sparse regression. To this end, it proposes an empirical Bayes framework grounded in convex penalties and log-concave priors. Methodologically, the approach leverages a unified proximal structure to optimize Monte Carlo sampling for efficient posterior uncertainty quantification, while introducing empirical Bayes calibration under affine information and geometry-aware posterior preconditioning techniques. Experiments on synthetic data demonstrate that the proposed method substantially improves both signal recovery accuracy and sampling efficiency. Furthermore, evaluations on a diabetes dataset validate the reliability of the estimated posterior uncertainties and highlight their practical utility in facilitating sparse decision-making.