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Abstract:
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We describe a novel approach to the specification of Bayesian Gaussian mixture models that eliminates the "label switching" problem. Label switching refers to the invariance of the posterior distribution for the component-specific parameters to relabeling of the components when an exchangeable prior is used. There are two common approaches to address this issue. The first breaks the exchangeability assumption by imposing artificial constraints on some model parameters (or specifies some other informative prior). The second approach relabels the MCMC samples generated to estimate the exchangeable model in a way that favors one specific relabeling of the components. Our approach forces a small number of observations, which we call the anchor points, to arise from prespecified components of the mixture. Specifying the anchor points is tantamount to specifying an informative, data-dependent prior, in which some observations are assumed to arise from a given component with probability one. We show that a careful choice of the anchor points can yield marginal posterior distributions for the component-specific parameters that are well-separated and interpretable.
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