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Bayesian Inference

Bayesian Inference - Bayesian Inference Lecture for...

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Bayesian Inference Lecture for Economics 245 Douglas G. Steigerwald UC Santa Barbara February 2011
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Con°dence Intervals Frequentist Inelegance ° B an estimator of β σ 2 = Var ( B ) ° P ( β ± 1 . 96 σ ² B ² β + 1 . 96 σ ) = . 95 ° b an estimate of β ° P ( β ± 1 . 96 σ ² b ² β + 1 . 96 σ ) = either 0 or 1 ° we are forced to use the concept of con°dence ° C ( β ± 1 . 96 σ ² b ² β + 1 . 96 σ ) = . 95 ° Bayesian - β is a random variable, no need to introduce con°dence
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Subjective Probability Bayesian Inelegance ° frequency de°nition - objective probability P ( A ) = lim n ! # f A g n ° A - obtain a 2 when rolling a die ° A 0 - rain on February 14, 2025 ° is A 0 repeatable? ° yes - model rain in February as a function of covariates ° no - Bayesian - introduce subjective probability ° subjective probability - much harder to de°ne ° not unique, common de°nition refers to fair odds of event occurring
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Bayesian Methods Important Developments and Distinctions Two key developments ° Stein±s paper on shrinkage estimators °
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