(27.) Similarly, if the answer were negative, posterior odds
of 999:1 would be far too low.
Thus, if the calculations are performed properly -- and we do not suggest that the NRC or its supporters miscalculate -- the posterior odds
must be the same under the NRC's likelihood ratio analysis and under our own.
The differences in log marginal likelihoods are so large that the posterior odds
of the DSGE model are practically zero.
He will have little incentive to pay close attention to the evidence presented at trial, because evidence of the defendant's guilt will not alter his original judgment, while evidence of the defendant's innocence, unless extremely powerful, will not push the posterior odds
into the range in which the judge would acquit the defendant.
Under the assumption that the two specifications have equal prior probability, the Bayes factor implies that the posterior odds
are 314 to 1 in favor of the 'full-information' specification.
Every evidence type 2 that is placed in Bayes Theorem will change, naturally, the Posterior Odds
If we define weight of evidence associated with x for a particular individual to be the ratio of posterior odds
(given x) of that individual to his or her prior odds (before observing x), then the above equation implies that LR = [f.sub.1](x)/[f.sub.2](x) is to be viewed as the weight of the evidence provided by x for [H.sub.1] for the individual making the probability assessments.
Many readers will already be aware of these concepts, although they may be more familiar with the terms positive predictive value (rather than posterior odds
) and pre-test probability (rather than prior odds).
If we had the same prior on each model, the posterior odds
ratio is the ratio of the marginal likelihoods:
Cogley and Sargent (2005) study an economy in which agents, facing model uncertainty, compute the posterior odds
ratios over three models and make decisions by Bayesian model averaging.
Taken literally, these differences imply posterior odds
that are in one case decisively in favor of, and in the other case against, the DSGE model.
The posterior odds
are then computed as the posterior probability of v being less than 30 divided by the posterior probability that v is greater than or equal to 30.