A general method for goodness-of-fit tests for arbitrary multivariate models

Goodness-of-fit tests are often used in data analysis to test the agreement of a model to a set of data. Out of the box tests that can target any proposed distribution model are only available in the univariate case. In this note I discuss how to build a goodness-of-fit test for arbitrary multivariate distributions or multivariate data generation models. The resulting tests perform an unbinned analysis and do not need any trials factor or look-elsewhere correction since the multivariate data can be analyzed all at once. The proposed distribution or generative model is used to transform the data to an uncorrelated space where the test is developed. Depending on the complexity of the model, it is possible to perform the transformation analytically or numerically with the help of a Normalizing Flow algorithm.