Enriched Stick-Breaking Processes for Functional Data

Abstract

In many applications involving functional data, prior information is available about the proportion of curves having different attributes. It is not straightforward to include such information in existing procedures for functional data analysis. Generalizing the functional Dirichlet process (FDP), we propose a class of stick-breaking priors for distributions of functions. These priors incorporate functional atoms drawn from constrained stochastic processes. The stick-breaking weights are specified to allow user-specified prior probabilities for curve attributes, with hyperpriors accommodating uncertainty. Compared with the FDP, the random distribution is enriched for curves having attributes known to be common. Theoretical properties are considered, methods are developed for posterior computation, and the approach is illustrated using data on temperature curves in menstrual cycles.

KEY WORDS:

• Functional data analysis
• Functional Dirichlet process
• Nonparametric Bayes
• Prior elicitation
• Random curves
• Random probability measure