论文标题
使用贝叶斯比较分区模型自动提取相互独立模式
Automated extraction of mutual independence patterns using Bayesian comparison of partition models
论文作者
论文摘要
相互独立性是统计中的一个关键概念，它表征了变量之间的结构关系。现有的研究相互独立性的方法依赖于两个竞争模型的定义，一个模型嵌套在另一个模型中，用于生成无效统计量的无效分布，通常是在渐近假设大型样本量的渐近假设下。因此，这些方法具有非常限制的应用范围。在当前的手稿中，我们建议将相互独立性的研究从假设驱动的任务中更改，该任务只能在非常具体的情况下应用于相互独立性模式内的盲人和自动搜索。为此，我们将问题视为在贝叶斯框架中解决的模型比较之一。在多元正常分布以及跨分类的多项式分布的情况下，我们显示了这种方法与现有方法之间的关系。我们提出了一个普通的马尔可夫链蒙特卡洛（MCMC）算法，以数值近似于所有相互独立模式的空间上的后验分布。该方法的相关性在综合数据以及两个真实数据集中证明，显示了该方法提供的独特见解。
Mutual independence is a key concept in statistics that characterizes the structural relationships between variables. Existing methods to investigate mutual independence rely on the definition of two competing models, one being nested into the other and used to generate a null distribution for a statistic of interest, usually under the asymptotic assumption of large sample size. As such, these methods have a very restricted scope of application. In the present manuscript, we propose to change the investigation of mutual independence from a hypothesis-driven task that can only be applied in very specific cases to a blind and automated search within patterns of mutual independence. To this end, we treat the issue as one of model comparison that we solve in a Bayesian framework. We show the relationship between such an approach and existing methods in the case of multivariate normal distributions as well as cross-classified multinomial distributions. We propose a general Markov chain Monte Carlo (MCMC) algorithm to numerically approximate the posterior distribution on the space of all patterns of mutual independence. The relevance of the method is demonstrated on synthetic data as well as two real datasets, showing the unique insight provided by this approach.
