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1、ProbabilityforlinguistsJohnGoldsmithApril20011.IntroductionProbabilityisasubjectnotwellknowntomostpeople--evenmathematicians,surprisingly.Itisplayinganincreasinglylargeroleincomputationallinguisticsandmachinelearning,andwillbeofgreatimportancetous.Ify
2、ou'vehadanyexposuretoprobabilityatall,you'relikelytothinkofcaseslikerollingdice.Ifyourollonedie,there'sa1in6chance--about0.166--ofrollinga"1",andlikewiseforthefiveothernormaloutcomesofrollingadie.Gamesofchance,likerollingdiceandtossingcoins,areimporta
3、ntillustrativecasesinmostintroductorypresentationsofwhatprobabilityisabout.Thisisonlynatural;thestudyofprobabilityarosethroughtheanalysisofgamesofchance,onlybecomingabitmorerespectablewhenitwasusedtoformtherationalbasisfortheinsuranceindustry.Butneith
4、eroftheseapplicationslendsitselftoquestionsoflinguistics,andlinguiststendtobeputoffbyexampleslikethese,exampleswhichseemtosuggestthatwetakeitforgrantedthattheutteranceofawordisabitliketherollofadie--whichit'snot,asweperfectlywellknow.Probabilityisbett
5、erthoughtofinanotherway.Weuseprobabilitytheoryinordertotalkinanexplicitandquantitativewayaboutthedegreeofcertainty,oruncertainty,thatwepossessaboutaquestion.Puttingitslightlydifferently,ifwewantedtodevelopatheoryofhowcertainaperfectlyrationalpersoncou
6、ldbeofaconclusioninthelightofspecificdata,we'dendupwithsomethingverymuchlikeprobabilitytheory.Andthat'showweshouldthinkofit.Let'stakeanexample.Manyofthelinguisticexamplesweconsiderwillbealongthelinesofwhataspeechrecognitionsystemmustdealwith,whichisto
7、say,thetaskofdeciding(orguessing)whatwordhasjustbeenuttered,givenknowledgeofwhattheprecedingstringofwordshasbeencomingoutofthespeaker'smouth.Wouldyoubewillingtoconsiderthefollowingsuggestions?LetussupposethatwehaveestablishedthatthepersonisspeakingEng
8、lish.Canwedrawanyconclusionsindependentofthesoundsthatthepersonisutteringatthismoment?Surelywecan.Wecanmakeanestimateoftheprobabilitythatthewordisinourdesk-topWebster'sDictionary,andwecanmakeanestimateoftheprobabilitythatthewordis"the",andanes
