Bayesian Inference

Bayesian Inference - Bayesian Inference Lecture for...

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Unformatted text preview: Bayesian Inference Lecture for Economics 245 Douglas G. Steigerwald UC Santa Barbara February 2011 Con&dence Intervals Frequentist Inelegance & B an estimator of β σ 2 = Var ( B ) & P ( β ¡ 1 . 96 σ ¢ B ¢ β + 1 . 96 σ ) = . 95 & b an estimate of β & P ( β ¡ 1 . 96 σ ¢ b ¢ β + 1 . 96 σ ) = either 0 or 1 & we are forced to use the concept of con&dence & C ( β ¡ 1 . 96 σ ¢ b ¢ β + 1 . 96 σ ) = . 95 & Bayesian - β is a random variable, no need to introduce con&dence 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- rain on February 14, 2025 & is A 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 Bayesian Methods Important Developments and Distinctions Two key developments & Stein&s paper on shrinkage estimators...
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This note was uploaded on 12/26/2011 for the course ECON 245a taught by Professor Staff during the Fall '08 term at UCSB.

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Bayesian Inference - Bayesian Inference Lecture for...

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