Premium
Bayesian assessment of goodness of fit against nonparametric alternatives
Author(s) -
Conigliani Caterina,
Castro J. Iván,
O'HAGAN Anthony
Publication year - 2000
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.2307/3315982
Subject(s) - goodness of fit , nonparametric statistics , chi square test , bayesian probability , bayes factor , parametric statistics , statistical hypothesis testing , mathematics , statistics , bayes' theorem , computer science , econometrics , data mining
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. Furthermore, as the test is based upon an approximation, it can only be used if there are sufficient data. In practice, these requirements are often wasteful of information and overly restrictive. The authors 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. They consider the extent to which their methodology can handle small data sets and continuous data without arbitrary grouping.