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Comparing two populations using Bayesian Fourier series density estimation

Abstract An important question in sciences is how to evaluate the similarity between two populations given independent samples from each of them. The most common approach to solve this is to use standard hypotheses tests. We propose an alternative method to compare two groups using a Bayesian nonparametric framework. The key idea is to measure the similarity between them by evaluating the distance between their associated densities. The nonparametric perspective makes it straightforward to assess the uncertainty about such distance without making strong assumptions about the generating processes. We provide both simulated and real examples to illustrate our method effectiveness.