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ProfileHiddenMarkovModelsMarkovChainAMarkovModelofDNAMutationsTwoUsesofaMarkovModelAMarkovModelGeneratingRandomDNASequencesAGoodIntroductiontoHMMADNAMotifRegularExpressionfortheMotifAProblemwithRegularExpressionAHiddenMarkovModelFirstThreeandLastThreeColumnsInsertionsPr(ACACATC)=0.8∙1∙0.8∙1∙0.8∙0.6∙0.4∙0.6∙1∙1∙0.8∙1∙0.8 ≈0.047TheProbabilitiesofSequencesAProblemwithProbabilitiesProbabilitiesandLog-oddsScoreslog-odds(ACACATC)=1.16+0+1.16+0+1.16-0.51+0.47-0.51+ 1.39+0+1.16+0+1.16 =6.64IfThereAreNoInsertionsAProblemwithProbabilitiesDerivedfromSimpleCountingPriorInformationThePseudocountMethodThePaperonDirichletMixturesDirichletDensityCompare2DirichletDensitieswith3ParametersDirichletMixtureTheProbabilitiesbyUsingaSingleDirichletDensityA9-componentDirichletMixtureTheAminoAcidsFavoredbytheComponentsTheProbabilitiesbyUsinga9-componentDirichletMixtureUseofPriorInformationTheBayesTheoremExampleExampleContinuedProfileHiddenMarkovModelsTheStructureofaProfileHMMAMultipleAlignmentTheMultipleAlignmentAPHMMUsingSimpleCountingAPHMMUsingPseudocountsofOneApplicationsofPHMMPHMMSoftware