{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T11:16:39Z","timestamp":1760267799713},"reference-count":13,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2022,3,26]],"date-time":"2022-03-26T00:00:00Z","timestamp":1648252800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2022,3,26]],"date-time":"2022-03-26T00:00:00Z","timestamp":1648252800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["BMC Bioinformatics"],"published-print":{"date-parts":[[2022,12]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:sec>\n                <jats:title>Background<\/jats:title>\n                <jats:p>A birth\u2013death process of which the births follow a hypoexponential distribution with <jats:italic>L<\/jats:italic> phases and are controlled by an on\/off mechanism, is a population process which we call the on\/off-seq-<jats:italic>L<\/jats:italic> process. It is a suitable model for the dynamics of a population of RNA molecules in a single living cell. Motivated by this biological application, our aim is to develop a statistical method to estimate the model parameters of the on\/off-seq-<jats:italic>L<\/jats:italic> process, based on observations of the population size at discrete time points, and to apply this method to real RNA data.<\/jats:p>\n              <\/jats:sec><jats:sec>\n                <jats:title>Methods<\/jats:title>\n                <jats:p>It is shown that the on\/off-seq-<jats:italic>L<\/jats:italic> process can be seen as a quasi birth\u2013death process, and an Erlangization technique can be used to approximate the corresponding likelihood function. An extensive simulation-based numerical study is carried out to investigate the performance of the resulting estimation method.<\/jats:p>\n              <\/jats:sec><jats:sec>\n                <jats:title>Results and conclusion<\/jats:title>\n                <jats:p>A statistical method is presented to find maximum likelihood estimates of the model parameters for the on\/off-seq-<jats:italic>L<\/jats:italic> process. Numerical complications related to the likelihood maximization are identified and analyzed, and solutions are presented. The proposed estimation method is a highly accurate method to find the parameter estimates. Based on real RNA data, the on\/off-seq-3 process emerges as the best model to describe RNA transcription.<\/jats:p>\n              <\/jats:sec>","DOI":"10.1186\/s12859-022-04638-6","type":"journal-article","created":{"date-parts":[[2022,3,29]],"date-time":"2022-03-29T00:04:03Z","timestamp":1648512243000},"update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Statistical inference for a quasi birth\u2013death model of RNA transcription"],"prefix":"10.1186","volume":"23","author":[{"given":"Mathisca","family":"de Gunst","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Michel","family":"Mandjes","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Birgit","family":"Sollie","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2022,3,26]]},"reference":[{"key":"4638_CR1","doi-asserted-by":"publisher","first-page":"267","DOI":"10.2143\/AST.32.2.1029","volume":"32","author":"S Asmussen","year":"2002","unstructured":"Asmussen S, Avram F, Usabel M. 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