使用 Autograd 对检验统计量的抽样分布进行建模
Modeling Sampling Distributions of Test Statistics with Autograd
AI总结：
本文研究利用 Autograd 对检验统计量的条件一维抽样分布进行建模，通过神经网络拟合 cdf 并求导获得密度近似，验证其作为似然比技巧替代方案的可行性。
摘要：
基于模拟的推断方法要求对基于已被压缩为标量检验统计量的观测值所构造的置信集具有正确的条件覆盖，这需要对检验统计量的 p 值函数或累积分布函数（cdf）进行精确建模。如果 cdf 模型（通常是深度神经网络）是检验统计量的函数，那么神经网络关于检验统计量的导数就提供了检验统计量抽样分布的近似。我们探索了这种对条件一维抽样分布进行建模的方法是否可以作为概率密度比方法（也称为似然比技巧）的可行替代方案。我们使用了相对简单但有效的神经网络模型，并通过多种方法对其预测不确定性进行了量化。
英文摘要：
Simulation-based inference methods that feature correct conditional coverage of confidence sets based on observations that have been compressed to a scalar test statistic require accurate modeling of either the p-value function or the cumulative distribution function (cdf) of the test statistic. If the model of the cdf, which is typically a deep neural network, is a function of the test statistic then the derivative of the neural network with respect to the test statistic furnishes an approximation of the sampling distribution of the test statistic. We explore whether this approach to modeling conditional 1-dimensional sampling distributions is a viable alternative to the probability density-ratio method, also known as the likelihood-ratio trick. Relatively simple, yet effective, neural network models are used whose predictive uncertainty is quantified through a variety of methods.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
