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
Markov counting models for correlated binary responses
Crawford FW, Zelterman D. Markov counting models for correlated binary responses. Biostatistics 2015, 16: 427-440. PMID: 25792624, PMCID: PMC5963474, DOI: 10.1093/biostatistics/kxv006.Peer-Reviewed Original ResearchConceptsExchangeable Bernoulli random variablesBernoulli random variablesCorrelated binary responsesMaximum likelihood estimatesInterpretable parameterizationsRandom variablesLikelihood estimatesCounting processDifferent cluster sizesBinary responsesCorrelated outcomesNatural wayCluster sizeBinary dataImproved fitPrevious modelsNew model
2014
On the distribution of interspecies correlation for Markov models of character evolution on Yule trees
Mulder WH, Crawford FW. On the distribution of interspecies correlation for Markov models of character evolution on Yule trees. Journal Of Theoretical Biology 2014, 364: 275-283. PMID: 25240905, PMCID: PMC4256168, DOI: 10.1016/j.jtbi.2014.09.016.Peer-Reviewed Original ResearchConceptsPhylogenetic treeYule treeProbability distributionPhylogenetic information contentContinuous-time modelPhylogenetic inference methodsOrnstein-Uhlenbeck modelCharacter evolutionPhylogenetic studiesNumber of mutationsTrait patternsRelated organismsStochastic modelNew speciesSimple continuous-time modelBrownian motionYule processEvolutionary processesPhenotypic changesMutation modelInference methodsSite patternsOptimal designSpeciationMutations
2013
Diversity, Disparity, and Evolutionary Rate Estimation for Unresolved Yule Trees
Crawford FW, Suchard MA. Diversity, Disparity, and Evolutionary Rate Estimation for Unresolved Yule Trees. Systematic Biology 2013, 62: 439-455. PMID: 23417679, PMCID: PMC3622899, DOI: 10.1093/sysbio/syt010.Peer-Reviewed Original ResearchConceptsPhylogenetic treePhylogenetic diversityTrait disparityEvolutionary relationshipsYule treeMammalian order CarnivoraPhenotypic trait valuesComparative evolutionary studiesEvolutionary rate estimationSet of taxaOrganism of interestTrait evolutionPhenotypic evolutionEvolutionary biologistsInferred phylogenyEvolutionary studiesUnresolved cladeTrait valuesMacroevolutionary studiesTrait dataRelated organismsOrder CarnivoraCladeBrownian motionBranch lengths
2011
Transition probabilities for general birth–death processes with applications in ecology, genetics, and evolution
Crawford FW, Suchard MA. Transition probabilities for general birth–death processes with applications in ecology, genetics, and evolution. Journal Of Mathematical Biology 2011, 65: 553-580. PMID: 21984359, PMCID: PMC3310285, DOI: 10.1007/s00285-011-0471-z.Peer-Reviewed Original Research