论文标题
广义重新定制的polya urn及其统计应用
Generalized Rescaled Polya urn and its statistical applications
论文作者
论文摘要
我们介绍了广义重新定制的polya（GRP）urn，该urn为群集数据的长期概率的良好性测试提供了一种生成模型，这是由于群集和相关性之间的独立性，这是由于增强机制在每个集群内部的独立性。我们将提出的测试应用于有关COVID-19大流行的Twitter帖子的数据集：用几句话，对于经典的卡方测试，数据对拒绝零假设的拒绝非常重要（每日长期情绪率保持恒定），但是，考虑到数据之间的相关性，引入的测试导致了不同的结论。除了统计应用外，我们指出，GRP urn是标准Eggenberger-Polya urn的简单变体，它具有适当的选择参数，显示了“局部”加强，几乎可以肯定，经验均值与确定性极限和预测性均值的不同渐近行为的融合。此外，该模型的研究提供了分析随机近似动态的机会，这些动力学在相关文献中是不寻常的。
We introduce the Generalized Rescaled Polya (GRP) urn, that provides a generative model for a chi-squared test of goodness of fit for the long-term probabilities of clustered data, with independence between clusters and correlation, due to a reinforcement mechanism, inside each cluster. We apply the proposed test to a data set of Twitter posts about COVID-19 pandemic: in a few words, for a classical chi-squared test the data result strongly significant for the rejection of the null hypothesis (the daily long-run sentiment rate remains constant), but, taking into account the correlation among data, the introduced test leads to a different conclusion. Beside the statistical application, we point out that the GRP urn is a simple variant of the standard Eggenberger-Polya urn, that, with suitable choices of the parameters, shows "local" reinforcement, almost sure convergence of the empirical mean to a deterministic limit and different asymptotic behaviours of the predictive mean. Moreover, the study of this model provides the opportunity to analyze stochastic approximation dynamics, that are unusual in the related literature.
