为什么写这篇文章呢,起因是在推导从SDE角度理解Diffusion Model时,在参考资料中出现了一个Tweedie’s formula,带着很多的疑问进而探究了一下经验贝叶斯估计的全貌。 贝叶斯估计的问题定义为根据一些观测数据 x 来估计未知参数 θ,用一个损失函数来衡量估计的准确性,如果用均方误差(MSE)来估计的话,我们将问题建模为:...
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...