Bayesian assessment of goodness of fit against nonparametric alternatives

The classical chi-square test of goodness of fit compares the hypothesis that data arise from some parametric family of distributions, against the nonparametric alternative that they arise from some other distribution. However, the chi-square test requires continuous data to be grouped into arbitrary categories, and, being based upon an approximation, it can only be used if there is sufficient data. In many practical situations these requirements are wasteful of information and overly restrictive respectively. We explore the use of the fractional Bayes factor to obtain a Bayesian alternative to the chi-square test when no specific prior information is available, including consideration of the extent to which it can handle small data sets and continuous data without arbitrary grouping. -