標(biāo)題：Applications of Stein’s method to sums of locally dependent r.v.’s
報(bào)告時(shí)間：2024年08月15日（星期四）14:00-15:00
報(bào)告地點(diǎn)：人民大街校區(qū)數(shù)學(xué)與統(tǒng)計(jì)學(xué)院415教室
主講人：蘇中根
主辦單位：數(shù)學(xué)與統(tǒng)計(jì)學(xué)院
報(bào)告內(nèi)容簡(jiǎn)介：
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.
主講人簡(jiǎn)介：
蘇中根，浙江大學(xué)數(shù)學(xué)科學(xué)學(xué)院教授，博士生導(dǎo)師。1995年獲復(fù)旦大學(xué)博士學(xué)位，主要從事概率極限理論及其應(yīng)用研究，曾主持多項(xiàng)國(guó)家自然科學(xué)基金項(xiàng)目，并獲教育部科技進(jìn)步二等獎(jiǎng)和浙江省自然科學(xué)二等獎(jiǎng)，寶鋼優(yōu)秀教師獎(jiǎng)。 合作（與林正炎、陸傳榮）編著的《概率極限理論基礎(chǔ)》（第二版）2021年獲首屆全國(guó)優(yōu)秀教材二等獎(jiǎng)。
