报告题目：Statistical Identification of Markov Chain

报告人：向绪言 教授

时间：2016-05-08

地点：数学与统计学院一楼报告厅

摘要：The study of Markov chains usually has an assumption with known density matrix. However the issue on the statistical identi_cation of Markov chains is an inversion process to identify its unknown density matrix, which has very power realistic applications. The density matrix is identi_ed by statistical and probabilistic method, based on the observation at the motion of the underlying Markov chain. Three types of Markov chains with condition on reversibility, stationarity (non-reversibility) and Markovian environment are discussed. As example, the single ion channels with the underlying scheme can be ki- netically modelled as (aggregated) homogeneous continuous-time Markov chain. A very important task is how to identify the transition rates of single ion chan- nels by a small number of states (i.e. identify the Q-matrix of the underlying Markov chain). A Markov chain inversion approach (MCIA) is developed to perform a di_cult inversion to identify the transition rates from the parame- ters characterizing the lifetime (sojourn time and hitting time) distributions at a small number of states, although it is straightforward to derive the lifetime distribution. The general explicit constraints relating the parameters of the life- time distribution to the transition rates are derived. The transition rates can be obtained with a computer program.

报告时间：5月8日上午8：30

报告人简介：

向绪言，博士，教授，硕士生导师，湖南文理学院数学与计算科学学院院长；湖南省新世纪“121人才工程”三层次人选，常德市“十百千”人才工程二层次人选，湖南省青年骨干教师，湖南省数学会常务理事，常德市数学会副理事长；湖南省综合评标专家，常德市政府采购评审专家，常德市电子政务咨询专家。

主要从事随机过程统计、计算及应用（生物信息、神经网络、随机计算与智能系统）方向的科研工作，在国际刊物《J. Phys. A: Math. and Gen.》、《Applied Mathematical Modelling》、《Soft Computing》等发表论文40余篇，20余篇被SCI、EI等收录，获湖南省自然科学优秀论文奖、人大复印资料全文转载，并获首届中华优秀出版论文奖。主持教育部留学回国人员科研启动基金、湖南省自然科学基金、湖南省教育厅优秀青年基金等省校级科研课题10余项，主持湖南省教学改革立项课题等质量工程与教学改革项目研究。