Introductionto BayesianStatisticsand anApplicationTimothy M.BahrIntroductionDefinitionsBayesianStatisticsMicroarraysConfoundedExperimentsModelGibbsSamplingApplicationIntroduction to Bayesian Statisticsand an ApplicationUnconfounding the Confounded: SeparatingTreatment and Batch Effects in ConfoundedMicroarray ExperimentsTimothy M. BahrDepartment of StatisticsBrigham Young UniversityMarch 16, 2009Introductionto BayesianStatisticsand anApplicationTimothy M.BahrIntroductionDefinitionsBayesianStatisticsMicroarraysConfoundedExperimentsModelGibbsSamplingApplicationIntroductionWho am I?Tim Bahr, Undergrad...I22, B.S. in Statistics,emphasis: BiostatIMy first intro to Statisticsin High SchoolIFascination with theNumerical Patterns inScienceIFuture GoalsIntroductionto BayesianStatisticsand anApplicationTimothy M.BahrIntroductionDefinitionsBayesianStatisticsMicroarraysConfoundedExperimentsModelGibbsSamplingApplicationIntroductionWho am I?Tim Bahr, Undergrad...I22, B.S. in Statistics,emphasis: BiostatIMy first intro to Statisticsin High SchoolIFascination with theNumerical Patterns inScienceIFuture GoalsIntroductionto BayesianStatisticsand anApplicationTimothy M.BahrIntroductionDefinitionsBayesianStatisticsMicroarraysConfoundedExperimentsModelGibbsSamplingApplicationIntroductionWho am I?Tim Bahr, Undergrad...I22, B.S. in Statistics,emphasis: BiostatIMy first intro to Statisticsin High SchoolIFascination with theNumerical Patterns inScienceIFuture GoalsIntroductionto BayesianStatisticsand anApplicationTimothy M.BahrIntroductionDefinitionsBayesianStatisticsMicroarraysConfoundedExperimentsModelGibbsSamplingApplicationIntroductionWho am I?Tim Bahr, Undergrad...I22, B.S. in Statistics,emphasis: BiostatIMy first intro to Statisticsin High SchoolIFascination with theNumerical Patterns inScienceIFuture GoalsIntroductionto BayesianStatisticsand anApplicationTimothy M.BahrIntroductionDefinitionsBayesianStatisticsMicroarraysConfoundedExperimentsModelGibbsSamplingApplicationIntroductionWho am I?Tim Bahr, Undergrad...I22, B.S. in Statistics,emphasis: BiostatIMy first intro to Statisticsin High SchoolIFascination with theNumerical Patterns inScienceIFuture GoalsIntroductionto BayesianStatisticsand anApplicationTimothy M.BahrIntroductionDefinitionsBayesianStatisticsMicroarraysConfoundedExperimentsModelGibbsSamplingApplicationIntroductionWho are you?BioinformaticsIMajors?IMath/Stat Background?IMicroarrays?IResearch?IWhy Bioinformatics?ICan I tell you what I thinkabout Bioinformatics?Introductionto BayesianStatisticsand anApplicationTimothy M.BahrIntroductionDefinitionsBayesianStatisticsMicroarraysConfoundedExperimentsModelGibbsSamplingApplicationDefinitionsIBayesian Statistics >>> statistical inferences onexperimental data + prior knowledge.IClassical (Frequentist) Statistics >>> data fromobservations or experiments only.IPrior Distribution: The distribution we assume ourparameters come from.IGibbs Sampling (simplification): An algorithm thatallows us to give interatively infer point estimates for“random” parameters.Introductionto BayesianStatisticsand anApplicationTimothy M.BahrIntroductionDefinitionsBayesianStatisticsMicroarraysConfoundedExperimentsModelGibbsSamplingApplicationDefinitionsIBayesian Statistics >>> statistical inferences onexperimental data + prior knowledge.IClassical (Frequentist) Statistics >>> data fromobservations or experiments only.IPrior Distribution: The distribution we assume ourparameters come from.IGibbs Sampling (simplification): An algorithm thatallows us to give interatively infer point estimates for“random” parameters.Introductionto BayesianStatisticsand anApplicationTimothy M.BahrIntroductionDefinitionsBayesianStatisticsMicroarraysConfoundedExperimentsModelGibbsSamplingApplicationDefinitionsIBayesian Statistics >>> statistical inferences onexperimental data + prior knowledge.IClassical (Frequentist) Statistics >>> data fromobservations or experiments only.IPrior Distribution: The distribution we assume ourparameters come from.IGibbs Sampling (simplification): An algorithm thatallows us to give interatively infer point estimates for“random” parameters.Introductionto BayesianStatisticsand anApplicationTimothy M.BahrIntroductionDefinitionsBayesianStatisticsMicroarraysConfoundedExperimentsModelGibbsSamplingApplicationDefinitionsIBayesian Statistics >>> statistical inferences onexperimental data + prior knowledge.IClassical (Frequentist) Statistics >>> data fromobservations or experiments only.IPrior Distribution: The distribution we assume ourparameters come from.IGibbs Sampling (simplification): An algorithm thatallows us to give interatively infer point estimates for“random” parameters.Introductionto BayesianStatisticsand anApplicationTimothy M.BahrIntroductionDefinitionsBayesianStatisticsMicroarraysConfoundedExperimentsModelGibbsSamplingApplicationDefinitionsIBayesian Statistics >>> statistical inferences onexperimental data + prior knowledge.IClassical (Frequentist) Statistics >>> data fromobservations or experiments only.IPrior Distribution: The distribution we assume ourparameters come from.IGibbs Sampling (simplification): An algorithm thatallows us to give interatively infer point estimates for“random” parameters.Introductionto BayesianStatisticsand anApplicationTimothy M.BahrIntroductionDefinitionsBayesianStatisticsMicroarraysConfoundedExperimentsModelGibbsSamplingApplicationDefinitionsIBiostatistics: The application of statistics to a widerange of topics in biology.IGene Expression Microarray: A high-throughputtechnology in molecular biology used to detect geneexpression levels in a cellular sample.IConfounded Experiment: when two or more variablesvary together so that it is impossible to separatetheir unique effects.Introductionto BayesianStatisticsand anApplicationTimothy M.BahrIntroductionDefinitionsBayesianStatisticsMicroarraysConfoundedExperimentsModelGibbsSamplingApplicationDefinitionsIBiostatistics: The application of statistics to a widerange of topics in biology.IGene Expression Microarray: A high-throughputtechnology in molecular biology used to detect geneexpression levels in a cellular sample.IConfounded Experiment: when two or more variablesvary together so that it is impossible to separatetheir unique effects.Introductionto BayesianStatisticsand anApplicationTimothy M.BahrIntroductionDefinitionsBayesianStatisticsMicroarraysConfoundedExperimentsModelGibbsSamplingApplicationDefinitionsIBiostatistics: The application of statistics to a