2018
Computational methods for birth‐death processes
Crawford FW, Ho LST, Suchard MA. Computational methods for birth‐death processes. Wiley Interdisciplinary Reviews Computational Statistics 2018, 10 PMID: 29942419, PMCID: PMC6014701, DOI: 10.1002/wics.1423.Peer-Reviewed Original ResearchBirth-death processStatistical inferenceGeneral birth–death processesFinite-time transitionBasic mathematical theoryNon-negative integersContinuous-time Markov chainMaximum likelihood estimationMathematical theoryTheoretical propertiesComputational difficultiesProbability distributionMarkov chainAnalytic expressionsEM algorithmEquilibrium probabilityStatistical workLikelihood estimationSimple caseLinear processRich varietyComputational methodsSimple linear processSummary statisticsInference
2014
Estimation for General Birth-Death Processes
Crawford FW, Minin VN, Suchard MA. Estimation for General Birth-Death Processes. Journal Of The American Statistical Association 2014, 109: 730-747. PMID: 25328261, PMCID: PMC4196218, DOI: 10.1080/01621459.2013.866565.Peer-Reviewed Original ResearchBirth-death processGeneral birth–death processesConditional expectationE-stepEM algorithmLinear birth-death processContinuous-time Markov chainTransition probabilitiesClosed-form solutionLinear modelMaximum likelihood estimatesMaximum likelihood estimationTime-consuming simulationsStatistical inferenceCostly simulationsData augmentation procedureMarkov chainDiscrete timeEfficient computationLikelihood estimatesNumber of particlesFraction representationLaplace transformLikelihood estimationAlgorithm convergence