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R. S. Protassov, D. A. van Dyk (Dept. of Statistics, Harvard University)
The likelihood ratio test (LRT) and F-test popularized in astrophysics by Bevington (Data Reduction and Error Analysis in the Physical Sciences) and Cash (1977, ApJ 228, 939), do not (even asymptotically) adhere to their nominal \chi2 and F distributions in many statistical tests commonly used in astrophysics. The many legitimate uses of the LRT (see, e.g., the examples given in Cash (1977)) notwithstanding, it can be impossible to compute the false positive rate of the LRT or related tests such as the F-test. For example, although Cash (1977) did not suggest the LRT for detecting a line profile in a spectral model, it has become common practice despite the lack of certain required mathematical regularity conditions. Contrary to common practice, the nominal distribution of the LRT statistic should not be used in these situations. In this paper, we characterize an important class of problems where the LRT fails, show the non-standard behavior of the test in this setting, and provide a Bayesian alternative to the LRT, i.e., posterior predictive p-values. We emphasize that there are many legitimate uses of the LRT in astrophysics, and even when the LRT is inappropriate, there remain several statistical alternatives (e.g., judicious use of error bars and Bayes factors). We illustrate this point in our analysis of GRB 970508 that was studied by Piro et al. in ApJ, 514:L73-L77, 1999.
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The author(s) of this abstract have provided an email address for comments about the abstract: protass@stat.harvard.edu