期刊
JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
卷 68, 期 -, 页码 179-199出版社
WILEY
DOI: 10.1111/j.1467-9868.2006.00539.x
关键词
Bayesian methods; functional data analysis; mixed models; model averaging; nonparametric regression; proteomics; wavelets
资金
- NCI NIH HHS [R01 CA107304-03, R01 CA107304-02, R01 CA107304, R37 CA057030, R01 CA057030, U01 CA057030] Funding Source: Medline
- NIEHS NIH HHS [P30 ES009106] Funding Source: Medline
- NATIONAL CANCER INSTITUTE [R01CA107304, R37CA057030, R01CA057030, U01CA057030] Funding Source: NIH RePORTER
- NATIONAL INSTITUTE OF ENVIRONMENTAL HEALTH SCIENCES [P30ES009106] Funding Source: NIH RePORTER
Increasingly, scientific studies yield functional data, in which the ideal units of observation are curves and the observed data consist of sets of curves that are sampled on a fine grid. We present new methodology that generalizes the linear mixed model to the functional mixed model framework, with model fitting done by using a Bayesian wavelet-based approach. This method is flexible, allowing functions of arbitrary form and the full range of fixed effects structures and between-curve covariance structures that are available in the mixed model framework. It yields nonparametric estimates of the fixed and random-effects functions as well as the various between-curve and within-curve covariance matrices. The functional fixed effects are adaptively regularized as a result of the non-linear shrinkage prior that is imposed on the fixed effects' wavelet coefficients, and the random-effect functions experience a form of adaptive regularization because of the separately estimated variance components for each wavelet coefficient. Because we have posterior samples for all model quantities, we can perform pointwise or joint Bayesian inference or prediction on the quantities of the model. The adaptiveness of the method makes it especially appropriate for modelling irregular functional data that are characterized by numerous local features like peaks.
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