Bernoulli mixtures

An interesting query on (or from) X validated: given a Bernoulli mixture where the weights are known and the probabilities are jointly drawn from a Dirichlet, what is the most efficient from running a Gibbs sampler including the latent variables to running a basic Metropolis-Hastings algorithm based on the mixture representation to running a collapsed Gibbs sampler that only samples the indicator variables… I provided a closed form expression for the collapsed target, but believe that the most efficient solution is based on the mixture representation!

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One Response to “Bernoulli mixtures”

Alberto L. Says:
November 12, 2019 at 11:59 am

Thanks for your answer to our question! The model appeared in the context of a Non-negative Matrix Factorization with a Bernoulli likelihood and Dirichlet priors (https://arxiv.org/abs/1812.06866). The Gibbs sampler we used is on Section 5. The closed-form expression you gently provided is in Appendix C.

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