Lecture 15 BM - GitHub Pages · Lecture 14: Bayesian Methods Theodoros Rekatsinas 1. Announcements...

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CS639: Data Management for Data Science Lecture 14: Bayesian Methods Theodoros Rekatsinas 1

Transcript of Lecture 15 BM - GitHub Pages · Lecture 14: Bayesian Methods Theodoros Rekatsinas 1. Announcements...

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CS639:DataManagementfor

DataScienceLecture14:BayesianMethods

TheodorosRekatsinas1

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Announcements

• WewillreleasegradesofMidtermbytheendofdaytoday.

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Today– BayesianMethods

• MotivationandIntroduction

• BayesTheorem

• Bayesianinference

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Motivation

• Statisticalinference:Drawingconclusionsbasedondatathatissubjecttorandomvariation(observationalerrorsandsamplingvariation)

• Sofarwesawthe“frequentists”pointofview.

• Bayesianinferenceprovidesadifferentwaytodrawconclusionsfromdata.

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BasicIdea

• Leveragepriorinformation andupdatepriorinformationwithnewdatatocreateaposteriorprobabilitydistribution.

• Threesteps:• Formprior(aprobabilitymodel)• Conditiononobserveddata(newdatafromyoursample)• Evaluatetheposteriordistribution

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BasicIdea

• “The centralfeature ofBayesianinference[is]the directquantificationofuncertainty”(Gelman etal.2014,4).• Lessemphasisonp-valuehypothesistesting.Moreemphasisontheconfidenceandprobabilityintervals.• Manyresearchersactuallyinterpret‘frequentist’confidenceintervals asif theywereBayesianprobabilityintervals.

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UncertaintyinFreq.andBayesianApproaches

• Bothinvolvethe estimationofunknownquantities ofinterest• Theestimatestheyproducehave differentinterpretations.

• Frequentist:95%Confidenceinterval:Repeatedsampleswillcontainthetrueparameterwithintheinterval95%ofthetime.

• Bayesian:95%Probability(credible)interval:Thereisa95% probability thattheunknownparameterisactuallyintheinterval.

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RandomVariables

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ProbabilityDistributions

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JointDistributions

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MarginalDistributions

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ConditionalProbabilities

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ConditionalProbabilities

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TheProductRule

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Bayes’Rule

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Bayes’Theorem

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Bayes’Theorem

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BayesianApproach

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BayesianLearning

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Wheredopriorscomefrom?

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Whendon’tpriormatter(much)?

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Whendon’tpriormatter(much)?

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Summary


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