论文标题
大规模随机实验的经验贝叶斯：光谱方法
Empirical Bayes for Large-scale Randomized Experiments: a Spectral Approach
论文作者
论文摘要
在许多行业中，大规模的随机实验有时称为A/B测试，越来越普遍。尽管经常通过频繁的$ t $检验对这种实验进行分析，但可以说，这样的分析不足：$ p $ - 价值很难解释，并且不容易纳入决策。作为替代方案，我们提出了一种经验贝叶斯方法，该方法假设治疗效应是从“真实先验”中实现的。这需要从先前的实验中推断出先验。在罗宾斯之后，我们估计了一个经验效应的边缘密度的家族，并由噪声量表索引。我们表明，这个家庭的特征是热方程式。我们基于傅立叶级数表示，可以通过凸优化进行有效计算的光谱最大似然估计。为了选择超参数并比较模型，我们描述了两个模型选择标准。我们在模拟和真实数据上演示了我们的方法，并将后验推断与先验的高斯混合模型下的方法进行比较。
Large-scale randomized experiments, sometimes called A/B tests, are increasingly prevalent in many industries. Though such experiments are often analyzed via frequentist $t$-tests, arguably such analyses are deficient: $p$-values are hard to interpret and not easily incorporated into decision-making. As an alternative, we propose an empirical Bayes approach, which assumes that the treatment effects are realized from a "true prior". This requires inferring the prior from previous experiments. Following Robbins, we estimate a family of marginal densities of empirical effects, indexed by the noise scale. We show that this family is characterized by the heat equation. We develop a spectral maximum likelihood estimate based on a Fourier series representation, which can be efficiently computed via convex optimization. In order to select hyperparameters and compare models, we describe two model selection criteria. We demonstrate our method on simulated and real data, and compare posterior inference to that under a Gaussian mixture model of the prior.
