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Abstract:
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Motivated by the problem of classifying hormone trajectories, we propose a flexible semiparametric Bayesian methodology for hierarchical functional data. By choosing a species sampling random probability measure for the distribution of coefficients in a spline model, a general class of nonparametric Bayesian methods for clustering of functional data is developed. Allowing the spline basis 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.
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