勷勤数学•专家报告

题      目：A class of Poisson--multiplication distributions for modeling count data with over-dispersion

报  告  人： 田国梁 教授  (邀请人：吴琴)

                                       南方科技大学

时      间： 11月7日  10：00-11:00

地     点：数科院东楼401

报告人简介:

        田国梁博士曾在美国马里兰大学从事医学统计研究六年, 在香港大学统计与精算学系任副教授八年, 从 2016 年 6 月至今在南方科技大学统计与数据科学系任教授、博士生导师。他目前的研究方向为 EM/MM/US 算法在统计中的应用、(0, 1) 区间上连续比例数据以及多元连续比例数据的统计分析、多元零膨胀计次数据分析, 在国外发表 160 余篇 SCI 论文、出版 3 本英文专著、在科学出版社出版英文教材 2 本。他曾是四个国际统计期刊的副主编, 目前是国际统计期刊 SII (Statistics and Its Interface) 的副主编。主持国家自然科学基金面上项目二项、主持深圳市稳定支持面上项目一项、参加国家自然科学基金重点项目一项。

摘      要：

       Count data with over-dispersion widely appears in natural sciences (e.g., biology and physics), social sciences and economics, medicine and health sciences, engineering and technology. Although the gamma-Poisson (mixture), generalized Poisson and double Poisson distributions were developed to address the issue of over-dispersion in count data, the number of existing discrete distributions is insufficient to meet the needs of fitting such complex count data. By decomposing the variance parameter in the Poisson distribution, in this paper, we propose a class of Poisson-multiplication (PM) distributions or a general Poisson-multiplication (Ge-PM) distribution with a natural statistical interpretation.  We provide five specific PM distributions that can be used to model count data with over-dispersion.  In the Ge-PM framework, we also develop five PM mean regression models for analyzing count data with covariates. We apply the normalized expectation-maximization (N-EM) algorithm aided by the upper--crossing/solution (US) algorithm to calculate maximum likelihood estimates of parameters. Simulation studies on model comparisons showed that the proposed five PM models extend the application scope of existing models, and a German health care demand data set is analyzed to illustrate the proposed methods.

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