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
2017
Birth/birth-death processes and their computable transition probabilities with biological applications
Ho LST, Xu J, Crawford FW, Minin VN, Suchard MA. Birth/birth-death processes and their computable transition probabilities with biological applications. Journal Of Mathematical Biology 2017, 76: 911-944. PMID: 28741177, PMCID: PMC5783825, DOI: 10.1007/s00285-017-1160-3.Peer-Reviewed Original ResearchMeSH KeywordsAlgorithmsAnimalsBayes TheoremCommunicable DiseasesComputational BiologyComputer SimulationEnglandEpidemicsHistory, 17th CenturyHost-Parasite InteractionsHumansLikelihood FunctionsMarkov ChainsMathematical ConceptsModels, BiologicalMonte Carlo MethodPlagueProbabilityStochastic ProcessesConceptsBirth-death processTransition probabilitiesFinite-time transition probabilitiesSIR modelMonte Carlo approximationJoint posterior distributionLikelihood-based inferenceApproximate Bayesian computationStatistical inferenceMatrix exponentiationPosterior distributionProcess approximationBivariate extensionBayesian computationFraction representationLaplace transformCorrelation structureUnivariate populationsRemoved (SIR) modelSmall systemsBivariate processEfficient algorithmApproximationDirect inferenceFast method
2015
Sex, lies and self-reported counts: Bayesian mixture models for heaping in longitudinal count data via birth–death processes
Crawford FW, Weiss RE, Suchard MA. Sex, lies and self-reported counts: Bayesian mixture models for heaping in longitudinal count data via birth–death processes. The Annals Of Applied Statistics 2015, 9: 572-596. PMID: 26500711, PMCID: PMC4617556, DOI: 10.1214/15-aoas809.Peer-Reviewed Original ResearchLongitudinal count dataImportant statistical problemSelf-reported countsBayesian mixture modelBirth-death processStatistical problemsBayesian hierarchical modelTrue distributionCount dataMixture modelInferential tasksHierarchical modelHeaping processParametersMultiplesModelInferenceEstimationDistributionGridProblemError
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