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Inverse probability weighting is also used to account for missing data when subjects with missing data cannot be included in the primary analysis<ref>Hernan, MA; Robins, JM (2006). "Estimating Causal Effects From Epidemiological Data". ''J Epidemiol Community Health''. '''60''' (7): 578–596. CiteSeerX 10.1.1.157.9366. doi:10.1136/jech.2004.029496. PMC 2652882. <nowiki>PMID 16790829</nowiki></ref>. With an estimate of the sampling probability, or the probability that the factor would be measured in another measurement, inverse probability weighting can be used to inflate the weight for subjects who are under-represented due to a large degree of missing data.

Inverse probability weighting is also used to account for missing data when subjects with missing data cannot be included in the primary analysis<ref>Hernan, MA; Robins, JM (2006). "Estimating Causal Effects From Epidemiological Data". ''J Epidemiol Community Health''. '''60''' (7): 578–596. CiteSeerX 10.1.1.157.9366. doi:10.1136/jech.2004.029496. PMC 2652882. <nowiki>PMID 16790829</nowiki></ref>. With an estimate of the sampling probability, or the probability that the factor would be measured in another measurement, inverse probability weighting can be used to inflate the weight for subjects who are under-represented due to a large degree of missing data.

【翻译】逆概率加权是一种统计技术，用于计算标准化到与收集数据的伪总体不同的统计量。研究设计与不同的抽样总体和总体的目标推断(目标总体)是常见的应用。可能存在阻碍研究人员直接从目标人群中取样的因素，如成本、时间或伦理问题。解决这个问题的方法是使用另一种设计策略，例如分层抽样。如果正确使用加权，可能会提高效率，减少未加权估计量的偏差。一个非常早期的加权估计是均值的 Horvitz-Thompson 估计。当抽样概率已知时，从目标总体中抽取抽样总体，然后利用这个概率的逆值对观测值进行加权。这种方法已经在各种框架下推广到统计学的许多方面。特别是，有加权的可能性，加权的估计方程，和加权的概率密度，其中大多数统计数据都是从中导出的。这些应用编纂了其他统计和估计理论，例如边际结构模型、标准死亡率和用于粗化或汇总数据的 EM 算法。当缺失数据的受试者不能被包括在主要分析中时，反概率加权也被用来解释缺失数据。通过对抽样概率的估计，或该因子在另一测量中被测量的概率，逆概率加权可以用来为由于大量数据缺失而代表性不足的受试者增加权重。

【翻译】逆概率加权是一种统计技术，用于计算标准化与收集数据的伪总体不同的统计量。研究设计与不同的抽样总体和总体的目标推断(目标总体)是常见的应用。可能存在阻碍研究人员直接从目标人群中采样的因素，如成本、时间或伦理问题。解决这个问题的方法是使用另一种设计策略，例如分层抽样。如果正确使用加权，可能会提高效率，减少未加权估计量的偏差。

 

一个非常早期的加权估计是霍维茨汤姆森估计量的均值估计。当抽样概率已知时，从目标总体中抽取抽样总体，然后利用这个概率的逆值对观测值进行加权。这种方法已经在各种框架下推广到统计学的许多方面。特别是，有加权的可能性，加权的估计方程，和加权的概率密度，其中大多数统计数据都是从中导出的。这些应用编纂了其他统计和估计理论，例如边际结构模型、标准死亡率和用于粗化或汇总数据的 EM 算法。

 

== Inverse Probability Weighted Estimator (IPWE) ==

== Inverse Probability Weighted Estimator (IPWE) ==

The inverse probability weighting estimator can be used to demonstrate causality when the researcher cannot conduct a controlled experiment but has observed data to model. Because it is assumed that the treatment is not randomly assigned, the goal is to estimate the counterfactual or potential outcome if all subjects in population were assigned either treatment.

The inverse probability weighting estimator can be used to demonstrate causality when the researcher cannot conduct a controlled experiment but has observed data to model. Because it is assumed that the treatment is not randomly assigned, the goal is to estimate the counterfactual or potential outcome if all subjects in population were assigned either treatment.

Suppose observed data are [[文件:Wiki-IPWE-Figure1.png]]  drawn i.i.d (independent and identically distributed) from unknown distribution P, where

Suppose observed data are [[文件:Wiki-IPWE-Figure1.png]]  <nowiki><math>\{\bigl(X_i,A_i,Y_i\bigr)\}^{n}_{i=1}</math></nowiki> drawn i.i.d (independent and identically distributed) from unknown distribution P, where

* [[文件:Wiki-IPWE-Figure2.png]] covariates

* [[文件:Wiki-IPWE-Figure2.png]] covariates