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June 2017 Bayesian Functional Data Modeling for Heterogeneous Volatility
Bin Zhu, David B. Dunson
Bayesian Anal. 12(2): 335-350 (June 2017). DOI: 10.1214/16-BA1004


Although there are many methods for functional data analysis, less emphasis is put on characterizing variability among volatilities of individual functions. In particular, certain individuals exhibit erratic swings in their trajectory while other individuals have more stable trajectories. There is evidence of such volatility heterogeneity in blood pressure trajectories during pregnancy, for example, and reason to suspect that volatility is a biologically important feature. Most functional data analysis models implicitly assume similar or identical smoothness of the individual functions, and hence can lead to misleading inferences on volatility and an inadequate representation of the functions. We propose a novel class of functional data analysis models characterized using hierarchical stochastic differential equations. We model the derivatives of a mean function and deviation functions using Gaussian processes, while also allowing covariate dependence including on the volatilities of the deviation functions. Following a Bayesian approach to inference, a Markov chain Monte Carlo algorithm is used for posterior computation. The methods are tested on simulated data and applied to blood pressure trajectories during pregnancy.


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Bin Zhu. David B. Dunson. "Bayesian Functional Data Modeling for Heterogeneous Volatility." Bayesian Anal. 12 (2) 335 - 350, June 2017.


Published: June 2017
First available in Project Euclid: 25 April 2016

zbMATH: 1384.62122
MathSciNet: MR3620736
Digital Object Identifier: 10.1214/16-BA1004

Keywords: Bayesian functional data analysis , Gaussian process , state space model , Stochastic differential equation , volatility heterogeneity


Vol.12 • No. 2 • June 2017
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