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.

Parameter clustering in Bayesian functional principal component analysis of neuroscientific data

“…Many of these works have focused on global clustering, where curves are clustered together for all their coefficients. [12][13][14][15][16][17][18][19] However, not only in neuroscientific data, but in many other types of functional data, curves might be characterized by regions of heterogeneous behaviors; 61 therefore, some authors have proposed alternative approaches that allow also for local differences in the clustering. 62,63 In the present study we moved from a global clustering of the data to a local clustering of fPC scores to address both the exploration of brain activity data and to improve curve reconstruction.…”

“…DP mixture models have also been used for clustering time series through the clustering of the relative coefficients in a basis expansion representation. Many of these works have focused on global clustering, where curves are clustered together for all their coefficients 12‐19 . However, not only in neuroscientific data, but in many other types of functional data, curves might be characterized by regions of heterogeneous behaviors; 61 therefore, some authors have proposed alternative approaches that allow also for local differences in the clustering 62,63 .…”

“…Different functional mixture models that cluster functions through clustering of the coefficients in a basis expansion have been proposed in the literature. [12][13][14][15][16][17][18][19] However, these works have focused on a global clustering of curves, without considering local differences as well as the possibility of a dynamic evolution of dependence among curves. In this work we use the principal component bases due to their straightforward interpretation and employ DP mixture priors for every eigendimension retained.…”

“…We develop a novel Bayesian fPCA model called parameter clustering fPCA (PCl‐fPCA) that makes use of a Dirichlet process (DP) mixture 9‐11 to model the prior distribution of the fPC scores. Different functional mixture models that cluster functions through clustering of the coefficients in a basis expansion have been proposed in the literature 12‐19 . However, these works have focused on a global clustering of curves, without considering local differences as well as the possibility of a dynamic evolution of dependence among curves.…”

Bayesian semiparametric customer base segmentation of mobile phone users based on longitudinal traffic data

“…In marketing segmentation application, one may be able to choose a parametric model for decreasing curves for problematic subjects, but it is much more difficult to parametrically describe all the possible curves that may characterize traffic of other subjects. To address a similar problem of studying basal body temperature of women during menstrual cycles, Scarpa and Dunson proposed to model the collection of distributions for different subjects as a mixture of a parametric component and a nonparametric contamination. In particular, the nonparametric component is characterized as a functional DP.…”