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However, a large p-value does not suggest that the two models are equivalent, but only that we lack evidence that they are not. " Third, the p-value itself offers no direct interpretation as a "weight of evidence," but only as a long-term probability (in a hypothetical repetition © 2000 by CRC Press LLC of the same experiment) of obtaining data at least as unusual as what was actually observed. 17) shows that it is nothing of the sort. 17). As a result, two experiments with identical likelihoods could result in different p-values if the two experiments were designed differently.

20) the ratio of the observed marginal densities for the two models. 20) we have which is nothing but the likelihood ratio between the two models. Hence, in the simple-versus-simple setting, the Bayes factor is precisely the odds in favor of over MZ given solely by the data. 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.

Moreover, even a perfect understanding of the model does not constitute a direct attack on the problem of predicting how the system under study will behave in the future - often the real goal of a statistical analysis. To this end, suppose that is a future observation, independent of y given the underlying . 5) thanks to the conditional independence of and y. This distribution summarizes the information concerning the likely value of a new observation, given the likelihood, the prior, and the data we have observed so far.

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A sensitivity analysis for nonrandomly missing categorical data arising from a national health disab by Baker S. G.

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