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Activity Number:
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259
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Type:
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Topic Contributed
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Date/Time:
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Tuesday, August 4, 2009 : 8:30 AM to 10:20 AM
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Sponsor:
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Section on Bayesian Statistical Science
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| Abstract - #304721 |
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Title:
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Stochastic Functional Data Analysis: A Bayesian Perspective
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Author(s):
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Bin Zhu*+ and Peter X.K. Song and Jeremy Taylor
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Companies:
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University of Michigan and University of Michigan and University of Michigan
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Address:
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1420 Washington Heights, Department of Biostatistics, Ann Arbor, MI, 48105,
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Keywords:
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Data augmentation ; Euler approximation ; MCMC ; Smoothing spline ; Simulation smoother ; Stochastic velocity model
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Abstract:
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We consider the problem of estimating an unknown smooth function given functional data. The unknown function is treated as the realization of a stochastic process, which is incorporated into a proposed diffusion model, called a stochastic velocity model. The resulting model offers great flexibility to capture the dynamic features of functional data, and allows straightforward and meaningful interpretation. The method of smoothing splines is connected to a special case of this approach. The likelihood of the model is derived with Euler approximation and data augmentation. Bayesian inference is carried out via a Markov Chain Monte Carlo algorithm with simulation smoother. The proposed model and method are illustrated using blood oxygenation-level dependent signal data, and prostate specific antigen data.
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