{"title":"马尔可夫跳跃过程的一般混合物的估计","authors":"Halina Frydman, Budhi Arta Surya","doi":"10.1002/cjs.11814","DOIUrl":null,"url":null,"abstract":"We propose a general mixture of Markov jump processes. The key novel feature of the proposed mixture is that the generator matrices of the Markov processes comprising the mixture are entirely unconstrained. The Markov processes are mixed with distributions that depend on the initial state of the mixture process. The maximum likelihood (ML) estimates of the mixture's parameters are obtained from continuous realizations of the mixture process and their standard errors from an explicit form of the observed Fisher information matrix, which simplifies the Louis (<jats:italic>Journal of the Royal Statistical Society Series B</jats:italic>, 44:226–233, 1982) general formula for the same matrix. The asymptotic properties of the ML estimators are also derived. A simulation study verifies the estimates' accuracy. The proposed mixture provides an exploratory tool for identifying the homogeneous subpopulations in a heterogeneous population. This is illustrated with an application to a medical dataset.","PeriodicalId":501595,"journal":{"name":"The Canadian Journal of Statistics","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2024-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Estimation in a general mixture of Markov jump processes\",\"authors\":\"Halina Frydman, Budhi Arta Surya\",\"doi\":\"10.1002/cjs.11814\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We propose a general mixture of Markov jump processes. The key novel feature of the proposed mixture is that the generator matrices of the Markov processes comprising the mixture are entirely unconstrained. The Markov processes are mixed with distributions that depend on the initial state of the mixture process. The maximum likelihood (ML) estimates of the mixture's parameters are obtained from continuous realizations of the mixture process and their standard errors from an explicit form of the observed Fisher information matrix, which simplifies the Louis (<jats:italic>Journal of the Royal Statistical Society Series B</jats:italic>, 44:226–233, 1982) general formula for the same matrix. The asymptotic properties of the ML estimators are also derived. A simulation study verifies the estimates' accuracy. The proposed mixture provides an exploratory tool for identifying the homogeneous subpopulations in a heterogeneous population. This is illustrated with an application to a medical dataset.\",\"PeriodicalId\":501595,\"journal\":{\"name\":\"The Canadian Journal of Statistics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-06-30\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"The Canadian Journal of Statistics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1002/cjs.11814\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"The Canadian Journal of Statistics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1002/cjs.11814","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
摘要
我们提出了马尔可夫跳跃过程的一般混合物。所提混合物的关键新特征是,构成混合物的马尔可夫过程的生成矩阵完全不受制约。马尔可夫过程的混合分布取决于混合过程的初始状态。混合物参数的最大似然法(ML)估计是从混合物过程的连续实化中获得的,其标准误差是从观察到的费雪信息矩阵的明确形式中获得的,这简化了路易斯(《皇家统计学会杂志》B 辑,44:226-233, 1982 年)关于同一矩阵的一般公式。此外,还得出了 ML 估计数的渐近特性。模拟研究验证了估计的准确性。所提出的混合物为识别异质人群中的同质子群提供了一种探索性工具。我们将通过对一个医疗数据集的应用来说明这一点。
Estimation in a general mixture of Markov jump processes
We propose a general mixture of Markov jump processes. The key novel feature of the proposed mixture is that the generator matrices of the Markov processes comprising the mixture are entirely unconstrained. The Markov processes are mixed with distributions that depend on the initial state of the mixture process. The maximum likelihood (ML) estimates of the mixture's parameters are obtained from continuous realizations of the mixture process and their standard errors from an explicit form of the observed Fisher information matrix, which simplifies the Louis (Journal of the Royal Statistical Society Series B, 44:226–233, 1982) general formula for the same matrix. The asymptotic properties of the ML estimators are also derived. A simulation study verifies the estimates' accuracy. The proposed mixture provides an exploratory tool for identifying the homogeneous subpopulations in a heterogeneous population. This is illustrated with an application to a medical dataset.