Frequentist and Bayesian statistics

《Frequentist and Bayesian statistics》由会员上传分享，免费在线阅读，更多相关内容在学术论文-天天文库。

1、FacultyofLifeSciencesFrequentistandBayesianstatisticsClausEkstrømE-mail:ekstrom@life.ku.dkOutline1FrequentistsandBayesians•Whatisaprobability?•Interpretationofresults/inference2Comparisons3MarkovchainMonteCarloSlide2—PhD(Aug23rd2011)—FrequentistandBayesianstatisticsWhatisaprobability?Twoschool

2、sinstatistics:frequentistsandBayesians.Slide3—PhD(Aug23rd2011)—FrequentistandBayesianstatisticsFrequentistschoolSchoolofJerzyNeyman,EgonPearsonandRonaldFischer.Slide4—PhD(Aug23rd2011)—FrequentistandBayesianstatisticsBayesianschool“School”ofThomasBayesP(D

3、H)·P(H)P(H

4、D)=P(D

5、H)·P(H)dHSlide5—PhD(

6、Aug23rd2011)—FrequentistandBayesianstatisticsFrequentistsFrequentiststalkaboutprobabilitiesinrelationtoexperimentswitharandomcomponent.Relativefrequencyofanevent,A,isdefinedasnumberofoutcomesconsistentwithAP(A)=numberofexperimentsTheprobabilityofeventAisthelimitingrelativefrequency.Relativefreq

7、uency0.00.20.40.60.81.0020406080100nSlide6—PhD(Aug23rd2011)—FrequentistandBayesianstatisticsFrequentists—2Thedefinitionrestrictsthethingswecanaddprobabilitiesto:WhatistheprobabilityoftherebeinglifeonMars100billionyearsago?Weassumethatthereisanunknownbutfixedunderlyingparameter,θ,forapopulation(i

8、.e.,themeanheightonDanishmen).Randomvariation(environmentalfactors,measurementerrors,...)meansthateachobservationdoesnotresultinthetruevalue.Slide7—PhD(Aug23rd2011)—FrequentistandBayesianstatisticsThemeta-experimentideaFrequentiststhinkofmeta-experimentsandconsiderthecurrentdatasetasasinglerea

9、lizationfromallpossibledatasets.Slide8—PhD(Aug23rd2011)—FrequentistandBayesianstatisticsThemeta-experimentideaFrequentiststhinkofmeta-experimentsandconsiderthecurrentdatasetasasinglerealizationfromallpossibledatasets.167.2cmSlide8—PhD(Aug23rd2011)—FrequentistandBayesianstatisticsThemeta-experi

10、mentideaFrequentiststhinkofmeta-experimentsandconsiderthecurrentdatasetasasinglerealizationfromallpossibledatasets.167.2cm175.5cmSlide8—PhD(Aug23rd2011)—FrequentistandBayesianstatisticsThemeta-experimentideaFrequentiststhinkofmeta-exper