2015/02/02 by Cecilia Earls, Giles Hooker, Earls, Cecilia +1 · 1 citation
Computer Science · Mathematics · #Bayesian Methods and Mixture Models #FOS: Computer and information sciences #Gaussian Processes and Bayesian Inference #Methodology (stat.ME) #Statistical Methods and Bayesian Inference
paper · pdf · doi:10.48550/arxiv.1502.00552
openalex publication_date 2015/02/02 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
We propose a model for functional data registration that compares favorably to the best methods of functional data registration currently available. It also extends current inferential capabilities for unregistered data by providing a flexible probabilistic framework that 1) allows for functional prediction in the context of registration and 2) can be adapted to include smoothing and registration in one model. The proposed inferential framework is a Bayesian hierarchical model where the registered functions are modeled as Gaussian processes. To address the computational demands of inference in high-dimensional Bayesian models, we propose an adapted form of the variational Bayes algorithm for approximate inference that performs similarly to MCMC sampling methods for well-defined problems. The efficiency of the adapted variational Bayes (AVB) algorithm allows variability in a predicted registered, warping, and unregistered function to be depicted separately via bootstrapping. Temperature data related to the el-niño phenomenon is used to demonstrate the unique inferential capabilities for prediction provided by this model.