Tree-structured Markov random fields with Poisson marginal distributions
提出了一类新的树结构马尔可夫随机场，其边际分布均为同均值的泊松分布且与依赖结构无关，便于应用，并给出了联合概率质量函数和生成函数的解析表达式。
A new family of tree-structured Markov random fields for a vector of discrete counting random variables is introduced. According to the characteristics of the family, the marginal distributions of the Markov random fields are all Poisson with the same mean, and are untied from the strength or structure of their built-in dependence. This key feature is uncommon for Markov random fields and most convenient for applications purposes. The specific properties of this new family confer a straightforward sampling procedure and analytic expressions for the joint probability mass function and the joint probability generating function of the vector of counting random variables, thus granting computational methods that scale well to vectors of high dimension. We study the distribution of the sum of random variables constituting a Markov random field from the proposed family, analyze a random variable’s individual contribution to that sum through expected allocations, and establish stochastic orderings to assess a wide understanding of their behavior.