{"title":"相位型老化模型推理相关估计的均匀化驱动算法。","authors":"Boquan Cheng, Rogemar Mamon","doi":"10.1007/s10985-022-09577-1","DOIUrl":null,"url":null,"abstract":"<p><p>We develop an efficient algorithm to compute the likelihood of the phase-type ageing model. The proposed algorithm uses the uniformisation method to stabilise the numerical calculation. It also utilises a vectorised formula to only calculate the necessary elements of the probability distribution. Our algorithm, with an error's upper bound, could be adjusted easily to tackle the likelihood calculation of the Coxian models. Furthermore, we compare the speed and the accuracy of the proposed algorithm with those of the traditional method using the matrix exponential. Our algorithm is faster and more accurate than the traditional method in calculating the likelihood. Based on our experiments, we recommend using 20 sets of randomly-generated initial values for the optimisation to get a reliable estimate for which the evaluated likelihood is close to the maximum likelihood.</p>","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"A uniformisation-driven algorithm for inference-related estimation of a phase-type ageing model.\",\"authors\":\"Boquan Cheng, Rogemar Mamon\",\"doi\":\"10.1007/s10985-022-09577-1\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p><p>We develop an efficient algorithm to compute the likelihood of the phase-type ageing model. The proposed algorithm uses the uniformisation method to stabilise the numerical calculation. It also utilises a vectorised formula to only calculate the necessary elements of the probability distribution. Our algorithm, with an error's upper bound, could be adjusted easily to tackle the likelihood calculation of the Coxian models. Furthermore, we compare the speed and the accuracy of the proposed algorithm with those of the traditional method using the matrix exponential. Our algorithm is faster and more accurate than the traditional method in calculating the likelihood. Based on our experiments, we recommend using 20 sets of randomly-generated initial values for the optimisation to get a reliable estimate for which the evaluated likelihood is close to the maximum likelihood.</p>\",\"PeriodicalId\":1,\"journal\":{\"name\":\"Accounts of Chemical Research\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":16.4000,\"publicationDate\":\"2023-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Accounts of Chemical Research\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s10985-022-09577-1\",\"RegionNum\":1,\"RegionCategory\":\"化学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"CHEMISTRY, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Accounts of Chemical Research","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s10985-022-09577-1","RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}
A uniformisation-driven algorithm for inference-related estimation of a phase-type ageing model.
We develop an efficient algorithm to compute the likelihood of the phase-type ageing model. The proposed algorithm uses the uniformisation method to stabilise the numerical calculation. It also utilises a vectorised formula to only calculate the necessary elements of the probability distribution. Our algorithm, with an error's upper bound, could be adjusted easily to tackle the likelihood calculation of the Coxian models. Furthermore, we compare the speed and the accuracy of the proposed algorithm with those of the traditional method using the matrix exponential. Our algorithm is faster and more accurate than the traditional method in calculating the likelihood. Based on our experiments, we recommend using 20 sets of randomly-generated initial values for the optimisation to get a reliable estimate for which the evaluated likelihood is close to the maximum likelihood.
期刊介绍：
Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance.
Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.
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