The test of homogeneity for normal mixtures has been used in various fields, but its theoretical understanding is limited because the parameter set for the null hypothesis corresponds to singular points in the parameter space. In this paper, we shed a light on this issue from a new perspective, variational Bayes, and offer a theory for testing homogeneity based on it. Conventional theory has not reveal the stochastic behavior of the variational free energy, which is necessary for constructing a hypothesis test, has remained unknown. We clarify it for the first time and construct a new test base on it. Numerical experiments show the validity of our results.

This paper studies a novel iterative detection algorithm for data detection in orthogonal frequency division multiplexing systems in the presence of phase noise (PHN) and channel estimation errors. By simplifying the maximum a posteriori algorithm based on the theory of variational inference, an optimization problem over variational free energy is formulated. After that, the estimation of data, PHN and channel state information is obtained jointly and iteratively. The simulations indicate the validity of this algorithm and show a better performance compared with the traditional schemes.

This paper deals with the problem of underdetermined blind source separation (BSS) where the number of sources is unknown. We propose a BSS approach that simultaneously estimates the number of sources, separates the sources based on the sparseness of speech, estimates the direction of arrival of each source, and performs permutation alignment. We confirmed experimentally that reasonably good separation was obtained with the present method without specifying the number of sources.