Econometrics-I-24

Part 24 bayesian estimation metropolis hastings a

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Unformatted text preview: Part 24: Bayesian Estimation Metropolis Hastings: A Draw of i &#152;&#152;&#152;&#152; &#152;™ 31/34 ,1 ,0 ,1 ,0 ,1 ,0 ,1 : ( ) ( ) ( ) a random draw from U(0,1) If U < R, use , During Gibbs iterations, draw controls acceptance rate. Try for i i r i i i i i Trial value d Posterior R Ms cancel Posterior U else keep β = β + β = β = β β β σ % % % .4. Part 24: Bayesian Estimation Application: Energy Suppliers p N=361 individuals, 2 to 12 hypothetical suppliers p X= (1) fixed rates, (2) contract length, (3) local (0,1), (4) well known company (0,1), (5) offer TOD rates (0,1), (6) offer seasonal rates (0,1). &#152;&#152;&#152;&#152; &#152;™ 32/34 Part 24: Bayesian Estimation Estimates: Mean of Individual i MSL Estimate Bayes Posterior Mean Price-1.04 (0.396)-1.04 (0.0374) Contract-0.208 (0.0240)-0.194 (0.0224) Local 2.40 (0.127) 2.41 (0.140) Well Known 1.74 (0.0927) 1.71 (0.100) TOD-9.94 (0.337)-10.0 (0.315) Seasonal-10.2 (0.333)-10.2 (0.310) &#152;&#152;&#152;&#152; &#152;™ 33/34 Part 24: Bayesian Estimation Reconciliation: A Theorem (Bernstein-Von Mises) p The posterior distribution converges to normal with covariance matrix equal to 1/N times the information matrix (same as classical MLE). (The distribution that is converging is the posterior, not the sampling distribution of the estimator of the posterior mean.) p The posterior mean (empirical) converges to the mode of the likelihood function. Same as the MLE. A proper prior disappears asymptotically. p Asymptotic sampling distribution of the posterior mean is the same as that of the MLE. &#152;&#152;&#152;&#152; &#152; 34/34...
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Part 24 Bayesian Estimation Metropolis Hastings A Draw of...

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