Nonparametric graphical model for counts.
Nonparametric graphical model for counts.
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发表时间：
2020-12
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通讯作者：
Dunson DB
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作者：
Roy A;Dunson DB
虽然多变量计数数据在许多应用领域都是常规收集的，但令人惊讶的是，很少有工作开发灵活的模型来表征它们的依赖结构。当兴趣集中在推断条件独立图时，这尤其如此。在这篇文章中，我们提出了一类新的两两马尔可夫随机场型模型的联合分布的多元计数向量。通过采用一种新的类型的转换，我们避免限制到非负依赖结构或通过截断诱导其他限制。采用贝叶斯方法进行推理，我们选择一个狄利克雷过程先验的随机效应的分布，以引起很大的灵活性的规格。提出了一种高效的马尔可夫链蒙特卡罗（MCMC）后验计算算法。我们证明了各种理论属性，包括后验一致性，并表明我们的COUNT非参数图形分析（CONGA）方法具有良好的性能，相对于竞争对手在模拟研究。该方法的动机是应用程序在小鼠神经元尖峰计数数据。
Although multivariate count data are routinely collected in many application areas, there is surprisingly little work developing flexible models for characterizing their dependence structure. This is particularly true when interest focuses on inferring the conditional independence graph. In this article, we propose a new class of pairwise Markov random field-type models for the joint distribution of a multivariate count vector. By employing a novel type of transformation, we avoid restricting to non-negative dependence structures or inducing other restrictions through truncations. Taking a Bayesian approach to inference, we choose a Dirichlet process prior for the distribution of a random effect to induce great flexibility in the specification. An efficient Markov chain Monte Carlo (MCMC) algorithm is developed for posterior computation. We prove various theoretical properties, including posterior consistency, and show that our COunt Nonparametric Graphical Analysis (CONGA) approach has good performance relative to competitors in simulation studies. The methods are motivated by an application to neuron spike count data in mice.