報(bào)告題目: Star Discrepancy For New Stratified Random Sampling I: Optimal Expected Star Discrepancy
報(bào)告時(shí)間:2022年2月24日(星期四), 20:00-21:00
報(bào)告地點(diǎn):廣東技術(shù)師范大學(xué)東校區(qū)工業(yè)中心506室
內(nèi)容摘要: We introduce a class of convex equivolume partitions. Expected star discrepancy results are compared for stratified samples under these partitions, including simple random samples. There are four main parts of ourresults. Firstly, among these newly designed partitions, there is one that minimizes the expected star discrepancy, thus we partly answer an open question in [F. Pausinger, S. Steinerberger, J. Complex. 2016]. Secondly, there are an infinite number of such class of partitions, they generate point sets with smaller expected discrepancy than classical jittered sampling for large sampling number, leading to an open question in [M. Kiderlen, F. Pausinger, Monatsh. Math.2021] being solved. Thirdly, we prove a strong partition principle and generalize the expected star discrepancy under these partition models from L2?discrepancy to star discrepancy, hence an open question in [M. Kiderlen, F. Pausinger, J.Complex. 2021] is answered. In the end, optimal expected star discrepancy upper bound under this class of partitions is given, which is better than using jittered sampling.
報(bào)告人簡介: 冼軍，男，博士，教授，博士生導(dǎo)師，國家優(yōu)秀青年基金獲得者，現(xiàn)任中山大學(xué)數(shù)學(xué)學(xué)院副院長、中國數(shù)學(xué)會(huì)理事、廣東省數(shù)學(xué)會(huì)理事、廣東省工業(yè)與應(yīng)用數(shù)學(xué)學(xué)會(huì)副理事長。2004年畢業(yè)于中山大學(xué)獲理學(xué)博士學(xué)位，同年進(jìn)入浙江大學(xué)博士后流動(dòng)站，2006年博士后出站至今在中山大學(xué)數(shù)學(xué)學(xué)院工作。主要研究方向?yàn)樾〔ǚ治雠c應(yīng)用調(diào)和分析、采樣理論及其在信號(hào)處理中的應(yīng)用。在ACHA，IP，JFAA，PAMS，JAT等國內(nèi)外主流專業(yè)期刊發(fā)表多篇關(guān)于信號(hào)的采樣與重構(gòu)的理論及其應(yīng)用的論文，部分結(jié)果獲得同行們的關(guān)注。曾作為項(xiàng)目負(fù)責(zé)人主持多項(xiàng)國家級(jí)和省部級(jí)基金項(xiàng)目，現(xiàn)作為項(xiàng)目負(fù)責(zé)人主持國家自然科學(xué)基金面上項(xiàng)目一項(xiàng)。2010年入選廣東省“千百十”人才工程培養(yǎng)計(jì)劃。
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