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Title: Gibbs sampling for finite mixtures with intractable likelihoods Authors:  Thomas Goodwin - University of Technology, Sydney (Australia) [presenting]
Matias Quiroz - University of Technology Sydney (Australia)
Christian Evenhuis - University of Technology Sydney (Australia)
Abstract: A finite mixture model is proposed where some of the components may have intractable likelihoods but are easy to simulate from. Such models include multivariate quantile distributions, such as the g-and-k distribution. To estimate the parameters we develop a Gibbs sampler with data augmentation, where the full conditional for the intractable component is sampled via ABC Markov Chain Monte Carlo. To sample the component indicators, we approximate the intractable likelihood via a semiparametric Bayesian synthetic likelihood approach. We demonstrate the model in a flow-cytometry application with highly irregular components.