Posterior simulation across nonparametric models for functional clustering
By choosing a species sampling random probability measure for the distribution of the basis coefficients, a general class of nonparametric Bayesian methods for clustering of functional data is developed. Allowing the basis functions to be unknown, one faces the problem of posterior simulation over a high-dimensional space of semiparametric models. To address this problem, we propose a novel Metropolis-Hastings algorithm for moving between models, with a nested generalized collapsed Gibbs sampler for updating the model parameters. Focusing on Dirichlet process priors for the distribution of the basis coefficients in multivariate linear spline models, we apply the approach to the problem of clustering of hormone trajectories. This approach allows the number of clusters and the shape of the trajectories within each cluster to be unknown. The methodology can be applied broadly to allow uncertainty in variable selection in semiparametric Bayes hierarchical models.
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