Detecting Multiple Model Components with the Likelihood Ratio Test

Details Detecting Multiple Model Components with the Likelihood Ratio Test Detecting Multiple Model Components with the Likelihood Ratio Test

May 2000

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2000aas...196.5401p&link_type=abstract

American Astronomical Society, 196th AAS Meeting, #54.01; Bulletin of the American Astronomical Society, Vol. 32, p.761

Astronomy and Astrophysics

Astrophysics

Scientific paper

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 χ2 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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