Bayesian Experimental Design - Mathematical Sciences Home Pages
Bayesian Experimental Design - Mathematical Sciences Home Pages
Bayesian Experimental Design - Mathematical Sciences Home Pages
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experimentoftenhelpinselectingimportantfeaturesthatdependonthespecicproblem. Indesigningaclinicaltrial,whereexperimentsaretobeperformedonpeople,thechoiceof and,ifnot,whattouseasacontroltreatment,isaproblemthatdoesnotariseindesigning thetreatmentstobecomparedisacentralethicalissue.Whetherornotaplaceboisethical Commonsense,availableresources,andknowledgeofthemotivationforcarryingoutthe<br />
aeldexperimenttocompareyieldsfromdierentfertilizercombinations.Notallaspects forthecontrolvariableshowevercanbesimplyexpressedinamathematicalframework. Thisproblemhasbeenconsideredatlengthinthescienticliteratureandisfocusedonin thispaper. ofexperimentaldesignaresusceptibletoabstractmathematicaltreatment.Choosingvalues<br />
precisespecicationofthereasontheexperimentisbeingconducted.Likemostareasof experimentationand,indeed,oftenmotivatesdoingtheexperiment,<strong>Bayesian</strong>methodsare ideallysuitedtocontributetoexperimentaldesign.<strong>Bayesian</strong>decisiontheoryalsomotivates collectionisrestrictedbylimitedresources.Becauseinformationisusuallyavailablepriorto Whendesigninganexperiment,decisionsmustbemadebeforedatacollection,anddata<br />
stilllagbehindthetheory.ApartfromFlournoy(1993)therearenotrue\casestudies" <strong>Bayesian</strong>statistics,<strong>Bayesian</strong>experimentaldesignhasgainedpopularityinthepasttwo decades.Butalsolikemanyareasof<strong>Bayesian</strong>statistics,applicationstoactualexperiments thatweknowof,where<strong>Bayesian</strong>ideashavebeenformallyappliedtothedesignofanactual presentedinthispaper. scienticexperimentbeforeitisdone.Thisisaveryimportantareaforfuturework.There arehoweverseveralexamplesofexamininganexperimentina<strong>Bayesian</strong>designframework afterithasbeendone:forexampleClyde,MullerandParmigiani(1994)andsomeexamples<br />
shouldthereforebeselectedtoachievesmallvariabilityfortheestimatorchosen.Much dependshoweveronwhatistobeestimated,andhowitwillbeestimated.Specifyingthe interestcanbeimprovedbyappropriatelyselectingthevaluesofthecontrolvariables.In estimationproblems,estimatorswithsmallvarianceareusuallydesirable.Controlvariables Thebasicideainexperimentaldesignisthatstatisticalinferenceaboutthequantitiesof<br />
purposeoftheexperimentgeneratesvariouscriteriaforthechoiceofadesign. Weaddressthefundamentalprinciplesofdesignbyprovidingageneral<strong>Bayesian</strong>decision 2
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