Applications of Stein’s method to sums of locally dependent r.v.’s

报告人：苏中根

报告地点：数学与统计学院415会议室

报告时间：2024年08月15日星期四14:00-15:00

报告摘要：

Stein’s method was first invented to estimate the error for normal   approximations of sums of dependent r.v.’s in 1972, and then was successfully   extended to poisson approximation for dependent trials 1975. Nowadays it has   been one of the most powerful tools in probability and statistics. In this   talk we report a recent work on applications of Stein’s method to sums of   locally dependent r.v.’s. In particular, consider a finite family of locally   dependent non-negative integer-valued random variables with finite third   order moments with W as their sum. Denote by M a three parameter random   variable, say the mixture of Bernoulli binomial distribution and Poisson   distribution, the mixture of negative binomial distribution and Poisson   distribution or the mixture of Poisson distributions. We use Stein’s method   to establish general upper error bounds for the total variation distance   between W and M, where three parameters in M are uniquely determined by the   first three moments of W. To illustrate, we study in detail a few of   well-known examples, among which are counting vertices of all edges point   inward, birthday problem, counting monochromatic edges in uniformly colored   graphs, and triangles and other subgraphs in the Erdos-Renyi random graph.   Through delicate analysis and computations, we obtain sharper upper error   bounds than existing results. This talk is based on recent joint works with   X.L. Wang.

主讲人简介：

苏中根，浙江大学数学科学学院教授，博士生导师。1995年获复旦大学博士学位，主要从事概率极限理论及其应用研究，曾主持多项国家自然科学基金项目，并获教育部科技进步二等奖和浙江省自然科学二等奖，宝钢优秀教师奖。 合作（与林正炎、陆传荣）编著的《概率极限理论基础》（第二版）2021年获首届全国优秀教材二等奖。