Bayesian inference on mixture models and their applications



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Texas A&M University


Mixture models are useful in describing a wide variety of random phenomena because of their flexibility in modeling. They have continued to receive increasing attention over the years from both a practical and theoretical point of view. In their applications, estimating the number of mixture components is often the main research objective or the first step toward it. Estimation of the number of mixture components heavily depends on the underlying distribution. As an extension of normal mixture models, we introduce a skew-normal mixture model and adapt the reversible jump Markov chain Monte Carlo algorithm to estimate the number of components with some applications to biological data. The reversible jump algorithm is also applied to the Cox proportional hazard model with frailty. We consider a regression model for the variance components in the proportional hazards frailty model. We propose a Bayesian model averaging procedure with a reversible jump Markov chain Monte Carlo step which selects the model automatically. The resulting regression coefficient estimates ignore the model uncertainty from the frailty distribution. Finally, the proposed model and the estimation procedure are illustrated with simulated example and real data.