A Bayesian Test for the Number of Modes in a Gaussian Mixture
This paper provides a Bayesian framework for testing the number of modes in a two-component Gaussian mixture. The test is done by first setting up conjugate priors and computing the corresponding posteriors, which are then integrated over the restricted subspace of unimodal parameter space for the mixture distribution, thus obtaining the prior and posterior probabilities of unimodality. Monte Carlo and Gibbs sampling methods are employed to numerically compute these probabilities due to the difficulty in finding analytical solutions. A conclusion on unimodality for the given data is arrived at based on the Bayes factor. Effectiveness of the proposed Bayes test is demonstrated via simulations, and applied to a practical data set on adult human heights in order to answer the question whether the combined height data for men and women is bimodal.