Bayes Vs the Lens a Theoretical Critique
Bayes Vs the Lens a Theoretical Critique
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(7) Maximum Likelihood Estimates : There is an alternative approach to all of this involving maximum likelihood estimators which might shed light on the empirical results obtained to date in the Lens studies. It also enables one to link the Bayesian approach more closely to the Lens approach.
Consider first an individual who is asked to come up with a best judgement of some parameter or dependent variable 9. Assume further that he or she is provided with a data vector X. Finally, assume, most i...mpor- tantly that the subject makes a utility free judgement. This is essen- tially what subjects are required to do in the Bayesian paradigm. Alter- natively stated, they are basically asked to choose that © which maximizes Pr(9\X, H) = Pr(©\H)Pr(x\e, H) / p r (X / H) where H is the prior information available to the subject. But, since the denominator of (8) is a constant this reduces to max Pr(©|H)Pr(X)e, H) © But this is precisely the maximum likelihood estimator.
Thus, the first result that we arrive at is that if the subject's priors are vague, the Bayesian decision rule collapses into a Maximum Likelihood Estimate.
What to read after Bayes Vs the Lens a Theoretical Critique?
You can find similar books in the "Read Also" column, or choose other free books by Michael F Van Breda to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
(7) Maximum Likelihood Estimates : There is an alternative approach to all of this involving maximum likelihood estimators which might shed light on the empirical results obtained to date in the Lens studies. It also enables one to link the Bayesian approach more closely to the Lens approach.
Consider first an individual who is asked to come up with a best judgement of some parameter or dependent variable 9. Assume further that he or she is provided with a data vector X. Finally, assume, most i...mpor- tantly that the subject makes a utility free judgement. This is essen- tially what subjects are required to do in the Bayesian paradigm. Alter- natively stated, they are basically asked to choose that © which maximizes Pr(9\X, H) = Pr(©\H)Pr(x\e, H) / p r (X / H) where H is the prior information available to the subject. But, since the denominator of (8) is a constant this reduces to max Pr(©|H)Pr(X)e, H) © But this is precisely the maximum likelihood estimator.
Thus, the first result that we arrive at is that if the subject's priors are vague, the Bayesian decision rule collapses into a Maximum Likelihood Estimate.
What to read after Bayes Vs the Lens a Theoretical Critique?
You can find similar books in the "Read Also" column, or choose other free books by Michael F Van Breda to read onlineMoreLess
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