Statistical inference for discretely observed Markov jump processes

• 成果类型: Article
• 署名作者: Bladt, M; Sorensen, M
• 署名单位: University of Copenhagen; Universidad Nacional Autonoma de Mexico
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1111/j.1467-9868.2005.00508.x
• 发表日期: 2005
• 页码: 395-410
• 关键词: maximum-likelihood-estimation; em algorithm; logarithm; semigroups; DIFFUSIONS; uniqueness; matrix

摘要

Likelihood inference for discretely observed Markov jump processes with finite state space is investigated. The existence and uniqueness of the maximum likelihood estimator of the intensity matrix are investigated. This topic is closely related to the imbedding problem for Markov chains. It is demonstrated that the maximum likelihood estimator can be found either by the EM algorithm or by a Markov chain Monte Carlo procedure. When the maximum likelihood estimator does not exist, an estimator can be obtained by using a penalized likelihood function or by the Markov chain Monte Carlo procedure with a suitable prior. The methodology and its implementation are illustrated by examples and simulation studies.