Lecture+6+Highlights

Lecture+6+Highlights - ECON 123A, Fall 2011, Lecture 6a...

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ECON 123A, Fall 2011, Lecture 6a Dale J. Poirier 6a-1 (5.1) Interval Estimation From the Bayesian standpoint, given a region ÷ d 1 and data y, it is meaningful to ask what is the probability that 2 lies in ÷ ? The answer is where " (0 < " < 1) is defined implicitly in (5.1). is known as a 1 - " Bayesian credible region . C There is no need to introduce the additional frequentist concept of “confidence.”
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ECON 123A, Fall 2011, Lecture 6a Dale J. Poirier 6a-2 Definition 5.1: Let p( 2 * y) be a posterior density function. Let 1 * d 1 satisfy (a) Pr( 2 0 1 * * y) = 1 - " , (b) For all 2 1 0 1 * and 2 2 ó 1 * , p( 2 1 * y) $ p( 2 2 * y). Then 1 * is defined to be a highest posterior density (HPD) region of content (1 - " ) for 2 . C Given a probability content of 1- " , the HPD region 1 * has the smallest possible volume in the parameter space 1 of any 1 - " Bayesian credible region. C Part (b) of Definition 5.1 implies that if [a, b] is a HPD interval, then p(a * y) = p(b * y).
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ECON 123A, Fall 2011, Lecture 6a Dale J. Poirier 6a-3 Exercise 5.1 (Graphical determination of an HPD interval): C Consider the posterior density in Figure 5.1. Use the graphical described earlier to obtain three sets of HPD intervals.
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ECON 123A, Fall 2011, Lecture 6a Dale J. Poirier 6a-4
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This note was uploaded on 12/13/2011 for the course ECON 123a taught by Professor Staff during the Fall '08 term at UC Irvine.

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Lecture+6+Highlights - ECON 123A, Fall 2011, Lecture 6a...

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