应数学系田波平教授邀请，美国印第安纳大学南本德分校关忠教授将于近日访问数学系并作报告。欢迎感兴趣的老师和同学参加。

报告1-2时间：2017年7月17日 下午14:00--17:00
报告1-2地点：一校区 格物楼503
 
Authors：
Zhong Guan, Department of Mathematical Sciences,
Indiana University South Bend, South Bend, Indiana 46634, U.S.A.
Jing Qin, Biostatistics Research Branch,  National Institute of Allergy and Infectious Diseases,  Bethesda, Maryland 20892, U.S.A
 
Talk 1：
Title：Optimal Combination of Biomarkers for Time-dependent ROC Estimation and Related Problems
Abstract：The receiver operating characteristic (ROC) curve is commonly used for assessing diagnostic test accuracy and for 
discriminatory ability of a medical diagnostic test in  distinguishing between diseases and non-diseased individuals. With the advance 
of technology, many genetic variables and biomarker variables are easily collected. The  most challenging problem is how to combine
clinical, genetic and biomarker variables together to predict disease status.   If one is interested in predicting $t$-year survival, however, 
the status of ``case'' (death) and ``control'' (survival) at the given $t$-year is unknown for those individuals who were censored before
$t$-year. To conduct an ROC analysis one has to impute those ambiguous  statuses. In this paper we study a maximum pseudo likelihood
method to estimate the underlying parameters and baseline distribution functions. The proposed approach produces  more efficient   and 
smoother estimate of the optimal time-dependent ROC curve and more stable
 
Talk 2：Introduction to Bernstein polynomial and iterated Bernstein polynomial 
Abstract：In this talk, I will give detailed introduction to Bernstein polynomial, it's properties, connection with probability distribution. The 
degree of approximation by Bernstein polynomial can be improved by repeated use of the Bernstein operation. This includes the so called
iterated Bernstein polynomial. The properties of the latter will be discussed with possible applications in statistics. 
 
 
报告3-4时间：2017年7月19日 上午9:00--12:00
报告3-4地点：一校区 正心楼111
 
Talk 3：Polynomial with positive coefficients--another generalization of Bernstein polynomial 
Abstract：In this talk, I will introduce another generalization of Bernstein polynomial approximation to non negative functions. Some properties
and it's applications in density estimation will be presented. 
 
Talk 4：Multivariate polynomial with positive coefficients and it's applications in statistics 
Abstract：In this talk I will introduce the multivariate generalization of the polynomial with positive coefficients. The degree of approximation and
applications in multivariate probability density estimation will be given.