有环的可逆马氏链的统计确认

数学物理学报 ›› 2020, Vol. 40 ›› Issue (6): 1682-1698.

有环的可逆马氏链的统计确认

向绪言^1,*(),付海琴²,周杰明³,邓迎春³,杨向群³

¹ 湖南文理学院数理学院 & 洞庭湖生态经济区发展与建设协同创新中心湖南常德 415000
² 湘潭大学数学与计算科学学院湖南湘潭 411105
³ 湖南师范大学数学与统计学院计算与随机数学教育部重点实验室长沙 410081

收稿日期:2020-03-08 出版日期:2020-12-26 发布日期:2020-12-29
通讯作者: 向绪言 E-mail:xyxiang2001@126.com
基金资助:
国家自然科学基金(11671132);湖南省教育厅科学研究重点项目(19A342);应用经济学湖南省应用特色学科

Statistical Identification of Reversible Markov Chain on Cyclic Graph

Xuyan Xiang^1,*(),Haiqin Fu²,Jieming Zhou³,Yingchun Deng³,Xiangqun Yang³

¹ Hunan Province Cooperative Innovation Center for The Construction and Development of Dongting Lake Ecological Economic Zone & School of Mathematics and Physics, Hunan University of Arts and Science, Hunan Changde 415000
² School of Mathematics and Computational Science, Xiangtan University, Hunan Xiangtan 411105
³ LCSM, Ministry of Education, School of Mathematics and Statistics, Hunan Normal University, Changsha 410081

Received:2020-03-08 Online:2020-12-26 Published:2020-12-29
Contact: Xuyan Xiang E-mail:xyxiang2001@126.com
Supported by:
the NSFC(11671132);the Key Scientific Research Project of Hunan Provincial Education Department(19A342);the Applied Economics of Hunan Province

摘要/Abstract

摘要：

马尔可夫链的统计确认探讨如何利用部分可观测数据来确认潜在的马尔可夫链的转移速率矩阵.作为最重要和最关键的一类可逆马尔可夫链, 有环(至少包含一个环)的可逆马尔可夫链的统计确认问题得到了研究.借助禁忌速率对可逆马尔可夫链击中时分布各阶导数的表达, 得到了确认其转移速率矩阵的必要条件, 给出了关于其充分性的一般性结论, 以及计算各转移速率的算法, 并通过数例验证了算法的正确性.

关键词: 可逆马尔可夫链, 转移速率矩阵, 统计确认, 有环图, 击中时

Abstract:

The statistical identification of Markov chain explores how to identify the transition rate matrix of the underlying Markov chain by partially observable data. SIMC on reversibly cyclic graphs (containing one cycle at least), as the most important and crucial class, is investigated then in this letter. As the differentials of hitting time distribution for a reversible Markov chain are expressed by taboo rates, the necessary condition is developed to identify the transition rate matrix and a general conclusion about sufficiency is provided. The proposed algorithms to exactly calculate all transition rates are developed. A numerical example is included to demonstrate the correctness of the proposed algorithms.

Key words: Reversible Markov chain, Transition rate matrix, Statistical identification, Cyclic graph, Hitting time

中图分类号:

O211.62

向绪言,付海琴,周杰明,邓迎春,杨向群. 有环的可逆马氏链的统计确认[J]. 数学物理学报, 2020, 40(6): 1682-1698.

Xuyan Xiang,Haiqin Fu,Jieming Zhou,Yingchun Deng,Xiangqun Yang. Statistical Identification of Reversible Markov Chain on Cyclic Graph[J]. Acta mathematica scientia,Series A, 2020, 40(6): 1682-1698.

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