The likelihood R(atio)-test

The likelihood R(atio)-test consists of a pairwise-comparison between forecasts.  The joint log-likelihood ratio of the observed catalog and two forecasts is computed and compared with the expected distribution of the joint log-likelihood ratio assuming that one of the forecasts is correct.  If the joint log-likelihood ratio of the observed catalog and the two forecasts under consideration is exceedingly low or exceedingly high relative to the expected distribution, this indicates that the forecast taken as correct can be rejected in favor of the other forecast.