By H. Charles Romesburg

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Bayesian analysis is predicated on such a belief in subjective probability, wherein we quantify whatever feelings (however vague) we may have about before we look at the data y in a distribution . 3)) with the resulting posterior distribution reflecting a blend of the information in the data and the prior. Historically, a major impediment to widespread use of the Bayesian paradigm has been that determination of the appropriate form of the prior (and perhaps the hyperprior h) is often an arduous task.

For more general hypotheses, this same "evidence given by the data" interpretation of BF is often used, though Lavine and Schervish (1999) show that a more accurate interpretation is that BF captures the change in the odds in favor of model 1 as we move from prior to posterior. In any event, in such cases, BF does depend which must be specified either as conveon the prior densities for the nient conjugate forms or by more careful elicitation methods. In this case, it becomes natural to ask whether "shortcut" methods exist that provide a rough measure of the evidence in favor of one model over another without reference to any prior distributions.

In any event, in such cases, BF does depend which must be specified either as conveon the prior densities for the nient conjugate forms or by more careful elicitation methods. In this case, it becomes natural to ask whether "shortcut" methods exist that provide a rough measure of the evidence in favor of one model over another without reference to any prior distributions. 21) where is the number of parameters in model i = 1, 2, and the usual likelihood ratio test statistic. BIC stands for Bayesian Information Criterion (though it is also known as the Schwarz Criterion), and denotes the change from Model 1 to Model 2.