电子商务中有限库存假设检验的一个基本问题
A fundamental problem of hypothesis testing with finite inventory in e-commerce
摘要：
在本文中，我们提请注意一个问题，这是经常被忽视或忽视的公司在网上环境中进行假设检验（A/B测试）。我们发现，在实验中的变体之间共享的有限库存上进行实验可能会导致高误报率，因为违反了组之间独立性的核心假设。我们提供了一个详细的分析问题的简化设置，其参数是由现实的情况。我们考虑的设置是一个$2$ -维随机游动在一个半无限带。它足够丰富，可以考虑有限的库存，但同时又足够简单，可以考虑假阳性概率的封闭形式。我们证明，高假阳性率可能会发生，并开发工具，适合帮助设计适当的测试在后续工作。我们的研究结果还表明，可能会出现高假阴性率。的证明依赖于一个功能的极限定理的$2$ -维随机游动在一个半无限条。
英文摘要：
In this paper, we draw attention to a problem that is often overlooked or ignored by companies practicing hypothesis testing (A/B testing) in online environments. We show that conducting experiments on limited inventory that is shared between variants in the experiment can lead to high false positive rates since the core assumption of independence between the groups is violated. We provide a detailed analysis of the problem in a simplified setting whose parameters are informed by realistic scenarios. The setting we consider is a $2$-dimensional random walk in a semi-infinite strip. It is rich enough to take a finite inventory into account, but is at the same time simple enough to allow for a closed form of the false-positive probability. We prove that high false-positive rates can occur, and develop tools that are suitable to help design adequate tests in follow-up work. Our results also show that high false-negative rates may occur. The proofs rely on a functional limit theorem for the $2$-dimensional random walk in a semi-infinite strip.
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