不精确Dirichlet过程及其在X< Y概率假设检验中的应用
Imprecise Dirichlet Process with application to the hypothesis test on the probability that X< Y
摘要：
狄利克雷过程（DP）是最流行的贝叶斯非参数模型之一。DP的一个公开问题是在缺乏先验信息的情况下如何选择其无穷维参数（基测度）。在这项工作中，我们提出了不精确的DP（IDP）-一个事先近乎无知的DP为基础的模型，不需要任何选择这个概率测度。它由一类DP组成，通过让DP的归一化基本度量在所有概率测度的集合中变化而获得。我们讨论了这种方法与贝叶斯鲁棒性的紧密联系，特别是通过概率集的先验近似无知建模。我们使用该模型对概率P（X<Y）进行贝叶斯假设检验。我们研究了IDP测试的理论特性（例如，渐近一致性），并将其与通常用作P（X< Y）检验的频率主义Mann-Whitney-Wilcoxon秩检验进行比较。特别是，我们将表明，我们的方法是更强大的，在这个意义上说，它是能够隔离的情况下，上述测试几乎是随机猜测。
英文摘要：
The Dirichlet process (DP) is one of the most popular Bayesian nonparametric models. An open problem with the DP is how to choose its infinite dimensional parameter (base measure) in case of lack of prior information. In this work we present the Imprecise DP (IDP) -- a prior near-ignorance DP-based model that does not require any choice of this probability measure. It consists of a class of DPs obtained by letting the normalized base measure of the DP vary in the set of all probability measures. We discuss the tight connections of this approach with Bayesian robustness and in particular prior near-ignorance modeling via sets of probabilities. We use this model to perform a Bayesian hypothesis test on the probability P(X<Y). We study the theoretical properties of the IDP test (e.g., asymptotic consistency), and compare it with the frequentist Mann-Whitney-Wilcoxon rank test that is commonly employed as a test on P(X< Y). In particular we will show that our method is more robust, in the sense that it is able to isolate instances in which the aforementioned test is virtually guessing at random.
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