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!

One Response to “Bernoulli mixtures”

  1. 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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