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首页> 外文期刊>Journal of the royal statistical society >Dirichlet process mixtures of order statistics with applications to retail analytics
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Dirichlet process mixtures of order statistics with applications to retail analytics

机译：Dirichlet将订单统计信息与零售分析应用程序混合处理

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The rise of 'big data' has led to the frequent need to process and store data sets containing large numbers of high dimensional observations. Because of storage restrictions, these observations might be recorded in a lossy-but-sparse manner, with information collapsed onto a few entries which are considered important. This results in informative missingness in the observed data. Our motivating application comes from retail analytics, where the behaviour of product sales is summarized by the price elasticity of each product with respect to a small number of its top competitors. The resulting data are vectors of order statistics, because only the top few entries are observed. Interest lies in characterizing the behaviour of a product's competitors, and clustering products based on how their competition is spread across the market. We develop non-parametric Bayesian methodology for modelling vectors of order statistics that utilizes a Dirichlet process mixture model with an exponentiated Weibull kernel. Our approach allows us added flexibility for the distribution of each vector, while providing parameters that characterize the decay of the leading entries. We implement our methods on a retail analytics data set of the cross-elasticity coefficients, and our analysis reveals distinct types of behaviour across the different products of interest.
机译：“大数据”的兴起导致经常需要处理和存储包含大量高维观测值的数据集。由于存储限制，这些观察结果可能以有损但稀疏的方式记录，并且信息会折叠到一些重要的条目上。这导致观察到的数据缺乏信息。我们的激励性应用来自零售分析，其中产品销售的行为通过相对于少数几个顶级竞争对手的每种产品的价格弹性来概括。结果数据是订单统计的向量，因为仅观察到了前几项。兴趣在于表征产品竞争对手的行为，并根据其竞争在整个市场中的分布情况对产品进行聚类。我们开发了非参数贝叶斯方法，用于对利用Dirichlet过程混合模型和指数Weibull核的订单统计向量进行建模。我们的方法使我们能够为每个矢量的分布增加灵活性，同时提供表征前导项衰减的参数。我们在具有交叉弹性系数的零售分析数据集上实施我们的方法，并且我们的分析揭示了感兴趣的不同产品之间行为的不同类型。

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