图对数线性模型性质的研究

摘要

By combining the Markov network with the log-linear models in contingency tables, the graphical log-linear models are established and the maximum likelihood estimate is studied.With the decomposition of the graphical models according to the maximum clique, the maximum likelihood estimate can be obtained.Thestructure and independence conditions of the five-dimensional graphical log-linear models are analyzed, and its formula of maximum likelihood estimation are obtained.%将马尔科夫网与对数线性模型的基本理论相结合,建立了图对数线性模型,并对模型参数的极大似然估计进行研究.根据极大团对图模型进行分解,即可得到极大似然估计.具体分析了五维随机变量的对数线性模型结构以及独立性条件,并且计算出其极大似然估计计算公式.