Model Comparison

Abstract

The availability of alternative models to fit a dataset requires a quantitative method for comparing the goodness of fit to different models. For Gaussian data, a lower reduced χ2 of one model with respect to another is already indicative of a better fit, but the outstanding question is whether the value is significantly lower, or whether a lower value can be just the result of statistical fluctuations. For this purpose we develop the distribution function of the F statistic, useful to compare the goodness of fit between two models and the need for an additional “nested” model component, and the Kolmogorov–Smirnov statistics, useful in providing a quantitative measure of the goodness of fit, and in comparing two datasets regardless of their fit to a specific model.