[2204.05615] Normalized Power Prior Bayesian Analysis - arXiv

However, in the original form of the joint power prior Bayesian approach, certain positive constants before the likelihood of the historical ... AccessiblearXiv DoyounavigatearXivusingascreenreaderorotherassistivetechnology?Areyouaprofessorwhohelpsstudentsdoso?Wewanttohearfromyou. PleaseconsidersigninguptoshareyourinsightsasweworktomakearXivevenmoreopen. ShareInsights Statistics>Methodology arXiv:2204.05615(stat) [Submittedon12Apr2022] Title:NormalizedPowerPriorBayesianAnalysis Authors:KeyingYe,ZifeiHan,YuyanDuan,TianyuBai DownloadPDF Abstract:Theelicitationofpowerpriors,basedontheavailabilityofhistorical data,isrealizedbyraisingthelikelihoodfunctionofthehistoricaldatato afractionalpower{\delta},whichquantifiesthedegreeofdiscountingofthe historicalinformationinmakinginferencewiththecurrentdata.When{\delta} isnotpre-specifiedandistreatedasrandom,itcanbeestimatedfromthe datausingBayesianupdatingparadigm.However,intheoriginalformofthe jointpowerpriorBayesianapproach,certainpositiveconstantsbeforethe likelihoodofthehistoricaldatacouldbemultipliedwhendifferentsettings ofsufficientstatisticsareemployed.Thiswouldchangethepowerpriorswith differentconstants,andhencethelikelihoodprincipleisviolated.Inthis article,weinvestigateanormalizedpowerpriorapproachwhichobeysthe likelihoodprincipleandisamodifiedformofthejointpowerprior.The optimalitypropertiesofthenormalizedpowerpriorinthesenseofminimizing theweightedKullback-Leiblerdivergenceisinvestigated.Byexaminingthe posteriorsofseveralcommonlyuseddistributions,weshowthatthediscrepancy betweenthehistoricalandthecurrentdatacanbewellquantifiedbythepower parameterunderthenormalizedpowerpriorsetting.Efficientalgorithmsto computethescalefactorisalsoproposed.Inaddition,weillustratetheuse ofthenormalizedpowerpriorBayesiananalysiswiththreedataexamples,and provideanimplementationwithanRpackageNPP. Subjects: Methodology(stat.ME);Applications(stat.AP) Citeas: arXiv:2204.05615[stat.ME]   (or arXiv:2204.05615v1[stat.ME]forthisversion) SubmissionhistoryFrom:ZifeiHan[viewemail] [v1] Tue,12Apr202208:23:18UTC(418KB) Full-textlinks: Download: PDF PostScript Otherformats (license) Currentbrowsecontext:stat.ME new | recent | 2204 Changetobrowseby: stat stat.AP References&Citations NASAADSGoogleScholar SemanticScholar a exportbibtexcitation Loading... Bibtexformattedcitation × loading... Dataprovidedby: Bookmark BibliographicTools BibliographicandCitationTools BibliographicExplorerToggle BibliographicExplorer(WhatistheExplorer?) LitmapsToggle Litmaps(WhatisLitmaps?) scite.aiToggle sciteSmartCitations(WhatareSmartCitations?) Code&Data CodeandDataAssociatedwiththisArticle arXivLinkstoCodeToggle arXivLinkstoCode&Data(WhatisLinkstoCode&Data?) Demos Demos ReplicateToggle Replicate(WhatisReplicate?) RelatedPapers RecommendersandSearchTools ConnectedPapersToggle ConnectedPapers(WhatisConnectedPapers?) Corerecommendertoggle CORERecommender(WhatisCORE?) AboutarXivLabs arXivLabs:experimentalprojectswithcommunitycollaborators arXivLabsisaframeworkthatallowscollaboratorstodevelopandsharenewarXivfeaturesdirectlyonourwebsite. BothindividualsandorganizationsthatworkwitharXivLabshaveembracedandacceptedourvaluesofopenness,community,excellence,anduserdataprivacy.arXiviscommittedtothesevaluesandonlyworkswithpartnersthatadheretothem. HaveanideaforaprojectthatwilladdvalueforarXiv'scommunity?LearnmoreaboutarXivLabsandhowtogetinvolved. Whichauthorsofthispaperareendorsers?| DisableMathJax(WhatisMathJax?)