Bayesian statistics

ProjectName1IndustrialHygieneMonitoringIntroductionToBayesianStatisticsDavePearson,DjonGentry,TimAllersProjectName2INTRODUCTIONTOBAYESIANSTATISTICSProjectName3IntroductiontoBayesianStatisticsWhatisBayesianStatistics?–Anapproachtostatisticsinwhichestimatesarebasedonasynthesisofapriordistributionandcurrentsampledata.–Beliefthatsomethingwillhappenisbasedonpastobservation.ProjectName4IntroductiontoBayesianStatisticsWhatisBayesianStatistics?–EverydayExample–Whenyoucrossaroad,youmayneedtodoafullanalysisofthedataconcerningoncomingtraffic(Howfast?Howbigisthegap?Doesthedriverlooklikeamaniac?Havetheyseenme?)butonethingyoudon'tconsider:oncethecarhasgonepastandIstepoutontheroad;whatisthechancethatitwillback-upandrunmeover–Inessencewe'veperformedaBayesiancalculationbasedonalifetimeofcrossingtheroad.Wehaveastrongbelief,basedonexperience,thatthecarwillnotbackup.ProjectName5IntroductiontoBayesianStatisticsWhyuseBayesianStatistics?–QuantifiablevalidationofpriorandfuturePPE&engineeringcontroldecisions–TopredictfutureexposuresandestablishPPEandengineeringcontrolrequirements–Typicalemployeeworks220days/year.4samplesrepresentsroughly2%oftheirannualexposureprofile–Statisticallyvaliddecisionmakingwithasfewas3samples–NewEHSStandardrequiresthatastatisticaltoolbeused–ProvidesaconsistentprocessforIHdecisionmaking–RiskManagementDecisionmakingbasedondefensibledataProjectName6From:PaulHewett,Ph.D.,CIH&JohnMulhaussen,Ph.D.,CIHProjectName7From:PaulHewett,Ph.D.,CIH&JohnMulhaussen,Ph.D.,CIHProjectName8From:PaulHewett,Ph.D.,CIH&JohnMulhaussen,Ph.D.,CIHProjectName9From:PaulHewett,Ph.D.,CIH&JohnMulhaussen,Ph.D.,CIHProjectName10From:PaulHewett,Ph.D.,CIH&JohnMulhaussen,Ph.D.,CIHProjectName11From:PaulHewett,Ph.D.,CIH&JohnMulhaussen,Ph.D.,CIHProjectName12TrivialProfessionalJudgment*Highly-ControlledWell-ControlledControlledPoorly-Controlled*QualitativeExposureAssessmentInput2BayesianDecisionAnalysisProjectName13Opening&RunningtheIHDataAnalystSoftwareProjectName14StartingtheIHDataAnalystProgramOnyourdesktopclicktheIHDataAnalysticon.EitherthisOrThisProjectName15TheProgramwillLaunchProjectName16InputFacilityInformationHereThefacilityinformationshouldreflecttheareawheretheIndustrialHygienemonitoringdatawasobtained.ProjectName17InputtheSubstanceInformationHere.Thissectionwouldincludethechemicalnameorifthemonitoringwasfornoise,theword“noise”Next,clickthedrop-downboxandselecttheunitofmeasure.ProjectName18InputIHDataHereInputthemonitoringdatafortheSubstancemonitoredinthe“Conc”column.Placea“Y”inthe“LOD”columnifthedataisalessthan()value.ProjectName19CrunchingtheNumbersClickthe“CalculateAll”buttononthetoolbar.ProjectName20IHDataInput&DecisionMakingProjectName21There’salotofStatsinthere!Helpmesiftthroughit.XO.95=95%ofyourdatashouldfallbelowthispoint.95%UCL=95%confidentthatanynewdatawillfallbelowthisnumberbasedonexistingdata.BDACharts–Indicationofhowwellcontrolledyourprocessis.PPECharts–J&JIHhasagreedtouse“75%or”fordecidingifPPEiswarrantedandtheappropriateAPF.ProjectName22Example1EthinylEstradiolAllsampleslessthanhalftheOELProjectName23Example1All5samples0.005XO.9595%UCLProjectName24Example1ProjectName2575%WhatIsYourDecision?ProjectName26Removed““DecisionProbabilityIncreasedProjectName27Addedonemoredatapoint.Now75%.FeelingmorecomfortablewithMakingdecisionfornorespiratorsDON’TFORGETTOCALCULATEALL!!!ProjectName28BydoublingtheoriginaldataResultedinProjectName29Doubledthedata.GreatercomfortinPPEdecisionNow84.5%ProjectName30ReportFormatWhatdoesthisprogramprovideasfarasfromawrittendocument?ProjectName31Report-Example1ProjectName32Report-Example1ProjectName33Report–Example1ProjectName34Report–Example1ProjectName35Example2Cobaltdust/fumeSampleresultsatorlessthanOELLookatyourdata.Whatisittryingtotellyou?Knowingwhentotakeadditionalsamplesandknowingwhentostopsamplingandimplementcontrols.ProjectName368datapointsrangingFrom1/10to1XOELProjectName37BDACharts=4PoorlyControlledProjectName38PPECharts=10XProjectName39DecisionMakingBDAChartsindicatePoorlyControlledPPEChartsindicatetheneedfor10XAPFWhatareyournextsteps?MakesureemployeesperformingthisworkareincludedintheRPP,MedSurveillance,andprovideaminimumof10xprotectionrespirators.Doyouthinkthatobtainingadditionalsampleswillhelpatthispoint?•ProbablyNotatthistimeEnhanceengineeringcontrols,thenre-sample•Afterengineeringcontrolshavebeenimplemented,newdatacollectedshouldbeseparatedfromthepreviousdatacollectedduringPoorControlsProjectName40Example38HrTWAvs.TaskDurationYouobtainsamplesduringaspecifictaskThetasklastsapproximately30minutesforthedayConfirmednootherexposuretothisorsimilarcompoundstheremainderofthedayCompoundbeingmeasureddoesnothaveacutehazardsassociatedwithitandthereisnoassignedSTEL.Whatdecisionsareyoumakingbasedonthesamplingresults?ProjectName41Example3–8Hrvs.TaskAllresultsarefromsampling30minutetaskResultsare1to3XOEL(NoSTEL)ProjectName42Example3–8Hrvs.TaskPPEChartsindicatetheneedForemploying10XAPFProjectName43Example3–8Hrvs.TaskHowever,ifoneweretoconvertresultsfromlabinto8HRTWA,assigning