A Bayesian Independence Test for Small Datasets

We propose a Bayesian test for independence among signals where only a small dataset is available. Traditional frequentist approaches often fail in this case due to inaccurate estimation of either the source statistical models or the threshold used by the test statistics. In addition, these frequentist methods cannot incorporate prior information into the computation of the test statistics. Our procedure renders parametric the nonparametric problem of testing for independence by quantizing the observed data samples into a table of cell counts. The test statistic is based on the likelihood of the observed cell counts under the independence hypothesis where the marginal cell probabilities are modeled by independent symmetric Dirichlet priors. We apply our Bayesian test to validate the solutions to the problem of blind source separation with small datasets using both synthetic and real-life benchmark data. The experimental results indicate that our approach can overcome the scarcity of data samples and significantly outperform the standard frequentist parametric methods with a proper selection of the prior parameters