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Unformatted text preview: 1 VIII. Model selection A. Marginal likelihood Suppose we’re trying to choose among a series of models: Model 1: p y  2 1 B Model M : p y  2 M where 2 m are possibly of different dimension The Bayesian might think in terms of an unobserved random variable: s 1 if Model 1 is true B s M if Model M is true 2 and assign prior probabilities = 1 Pr s 1 B = M Pr s M with associated priors on the parameters p 2 1  s 1 B p 2 M  s M From such a perspective, the probability that Model m is true given the data is p s m  y = m ; p y  2 m p 2 m  s m d 2 m ! j 1 M = j ; p y  2 j p 2 j  s j d 2 j q = m p m y ! j 1 M = j p j y The expression p m y ; p y  2 m p 2 m  s m d 2 m is sometimes called the "marginal likelihood" of Model m 3 The Bayesian would say that the data favor the model for which p s m  y is biggest. With diffuse priors = m 1/ M this is equivalent to choosing the model with the highest marginal likelihood. VIII. Model selection A. Marginal likelihood B. Schwarz criterion First let’s examine the behavior of p m y ; p y  2 m p 2 m  s m d 2 m as the sample size T gets large 4 Suppose log p y  2 !...
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This note was uploaded on 03/02/2012 for the course ECON 226 taught by Professor Jameshamilton during the Winter '09 term at UCSD.
 Winter '09
 JamesHamilton

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