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Lecture 2

Lecture 2. Frequentist vs Bayesian statistics. We can draw stronger conclusions from Bayesian statistics! Frequentist P- value : P( observed data or more extreme | H o ) Bayesian P- value : P(H o | data) Concerns about Bayesian inference

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Lecture 2

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  1. Lecture 2

  2. Frequentist vs Bayesian statistics • Wecandraw stronger conclusions from Bayesianstatistics! • Frequentist P-value: • P(observed data or moreextreme | Ho ) • Bayesian P-value: • P(Ho | data) • ConcernsaboutBayesianinference • Wehavetochoosea prior and it is oftenveryarbitrary. prior posterior likelihood

  3. A reindeerexample • The herdersgatherhundredsofreindeereachautumn • Save 20% of the heaviestcalves • Variation betweenyears • Theyhavetodecidedirectlyafterweighingwhethertokeep the calf or not

  4. Looking back at previousyearstheycanseethat the averageweight has been 45 kg • Butquitelargevariancebetweenyearsof 4.0 • The variancewithinyears is • LetX be the unkownweightof the firstincomingcalf; assumed normal • Will the firstcalfbelongto the top 20% thatday? • Weneedto make a guessof the meanweightthatday, ie

  5. Theory • Prior • Likelihood • Posterior mean • Easytoupdate

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