Week+3+Problem+Set+2011

Week+3+Problem+Set+2011 - 3. Are either of the following...

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Department of Economics Professor Dale J. Poirier University of California, Irvine October 27, 2011 ECON 123A Econometrics I Fall, 2011 Problem Set Week 3 1. Explain briefly the term “exchangeability. Does exchangeability imply independence? 2. Consider an experiment with a countable number of possible outcomes y 1 , y 2 , y 3 , . .. and two mutually exclusive and exhaustive statistical hypotheses H 1 and H 2 . Is the statement “Given one observation Y, the ex ante expected Bayes factor in favor of a false hypothesis is unity” true or false? Explain your answer.
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Unformatted text preview: 3. Are either of the following shaded horizontal areas a HPD region? Why or why not? (a) (b) 4. Consider a random sample of size T = 16 from a N( 2 , 11.25) distribution. Assume your prior beliefs are 2-N( , 11.25/ ), where = 1 and = 9. Finally, suppose the realized sample mean is = .25. (a) Find the posterior distribution 2 * y. (b) Find Pr( 2 > 0 * y). (c) Find a .95 HPD interval for 2 . (d) Consider the hypotheses H 1 : 2 # 1 and H 2 : 2 > 1. Find the posterior odds Pr(H 2 * y)/Pr(H 1 * y)....
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