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This entry for the 2018 MDPI English Writing Prize has been published as a chapter of "The Global Benefits of Open Research", edited by Martyn Rittman.

This short note presents results about the symmetric Jensen-Shannon divergence between two discrete mixture distributions p1 and p2. Specifically, for i=1,2, pi is the mixture of a common distribution q and a distribution p̃ i with mixture proportion λi. In general, p̃ 1≠p̃ 2 and λ1≠λ2. We provide experimental and theoretical insight to the behavior of the symmetric Jensen-Shannon divergence between p1 and p2 as the mixture proportions or the divergence between p̃ 1 and p̃ 2 change. We also provide insight into scenarios where the supports of the distributions p̃ 1, p̃ 2, and q do not coincide.