文章写作的起因是在推导从SDE角度理解Diffusion Model时，遇到了Tweedie’s formula，带着众多疑问，作者进一步探究了经验贝叶斯估计的全貌。贝叶斯估计问题定义为根据观测数据估计未知参数，用损失函数衡量估计准确性。若用均方误差(MSE)估计，则将问题建模为求解后验分布的均值。这被称为最小均方误差估计器min...
本文将深入探讨经验贝叶斯估计，包括Robbins、James-Stein和Tweedie的三种关键方法，以及它们在缺失物种估计中的应用实例。首先，经验贝叶斯估计是通过观测数据[公式]估计未知参数[公式]的过程，使用最小均方误差(MSE)作为评估标准。关键步骤是求解后验分布均值，需知道后验概率和似然函数，以及先验分布信息。经典...
Tweedie’s Formula and Selection Bias Bradley Efron ∗ Stanford University Abstract 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...
Tweedies formula, first reported by Robbins in 1956, offers a simple empirical Bayes approach for correcting selection bias. This article investigates its merits and limitations. In addition to the methodology, Tweedies formula raises more general questions concerning empirical Bayes theory, discussed ...
Tweedie’sFormulaandSelectionBiasBradleyEfron*StanfordUniversityAbstractWesupposethatthestatisticianobservessomelargenumberofestimateszi,eachwithitsownunobservedexpectationparameterμi.Thelargestfewofthezi’sarelikelytosubstantiallyoverestimatetheircorrespondingμi’s,thisbeinganexampleofselectionbias,orregressiontothemean...