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Bayesian nonparametric modeling for functional analysis of variance

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  • XuanLong Nguyen
  • Alan Gelfand

Abstract

Analysis of variance is a standard statistical modeling approach for comparing populations. The functional analysis setting envisions that mean functions are associated with the populations, customarily modeled using basis representations, and seeks to compare them. Here, we adopt the modeling approach of functions as realizations of stochastic processes. We extend the Gaussian process version to allow nonparametric specifications using Dirichlet process mixing. Several metrics are introduced for comparison of populations. Then we introduce a hierarchical Dirichlet process model which enables comparison of the population distributions, either directly or through functionals of interest using the foregoing metrics. The modeling is extended to allow us to switch the sampling scheme. There are still population level distributions but now we sample at levels of the functions, obtaining observations from potentially different individuals at different levels. We illustrate with both simulated data and a dataset of temperature versus depth measurements at different locations in the Atlantic Ocean. Copyright The Institute of Statistical Mathematics, Tokyo 2014

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  • XuanLong Nguyen & Alan Gelfand, 2014. "Bayesian nonparametric modeling for functional analysis of variance," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 66(3), pages 495-526, June.
    • Handle: RePEc:spr:aistmt:v:66:y:2014:i:3:p:495-526
    DOI: 10.1007/s10463-013-0436-7
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    References listed on IDEAS

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    1. Rappold, Ana Grohovac & Lavine, Michael & Lozier, Susan, 2007. "Subjective Likelihood for the Assessment of Trends in the Ocean's Mixed-Layer Depth," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 771-780, September.
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    1. Rebecca Graziani & Michele Guindani & Peter F. Thall, 2015. "Bayesian nonparametric estimation of targeted agent effects on biomarker change to predict clinical outcome," Biometrics, The International Biometric Society, vol. 71(1), pages 188-197, March.

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