论文标题
逆概率加权：从调查采样到证据估计
Inverse Probability Weighting: from Survey Sampling to Evidence Estimation
论文作者
论文摘要
我们考虑一类反概率权重（IPW）估计量的类别，包括在调查采样，因果推理和贝叶斯计算的证据估计中常规使用的流行Horvitz-Thompson和Hajek估计器。由于Basu [1988]和Wasserman [2004]的两个反例，我们重点关注这些估计值的“弱悖论”，并研究了两个天然贝叶斯对此问题的答案：一个基于分类和平滑的基于“贝叶斯筛子”的：“贝叶斯筛子”，另一个基于基于循环层次模型，可通过交换借用信息。我们通过模拟广泛的参数配置进行了模拟研究，将两个贝叶斯估计量的平方平方误差与Wasserman示例的IPW估计器进行了比较。我们还证明，在失踪的全面假设下，贝叶斯估计量的后验一致性，并表明它所需的对纳入概率的假设更少。我们还重新审查了改善或自适应IPW估计器将很有用的不同问题之间的联系，包括调查抽样，有条件的蒙特卡洛，riemannian总和，梯形规则和垂直可能性，以及因果关系中的平均治疗效果估计。
We consider the class of inverse probability weight (IPW) estimators, including the popular Horvitz-Thompson and Hajek estimators used routinely in survey sampling, causal inference and evidence estimation for Bayesian computation. We focus on the 'weak paradoxes' for these estimators due to two counterexamples by Basu [1988] and Wasserman [2004] and investigate the two natural Bayesian answers to this problem: one based on binning and smoothing : a 'Bayesian sieve' and the other based on a conjugate hierarchical model that allows borrowing information via exchangeability. We compare the mean squared errors for the two Bayesian estimators with the IPW estimators for Wasserman's example via simulation studies on a broad range of parameter configurations. We also prove posterior consistency for the Bayes estimators under missing-completely-at-random assumption and show that it requires fewer assumptions on the inclusion probabilities. We also revisit the connection between the different problems where improved or adaptive IPW estimators will be useful, including survey sampling, evidence estimation strategies such as Conditional Monte Carlo, Riemannian sum, Trapezoidal rules and vertical likelihood, as well as average treatment effect estimation in causal inference.
