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Hierarchical models for assessing variability among functions


  • Sam Behseta
  • Robert E. Kass
  • Garrick L. Wallstrom


In many applications of functional data analysis, summarising functional variation based on fits, without taking account of the estimation process, runs the risk of attributing the estimation variation to the functional variation, thereby overstating the latter. For example, the first eigenvalue of a sample covariance matrix computed from estimated functions may be biased upwards. We display a set of estimated neuronal Poisson-process intensity functions where this bias is substantial, and we discuss two methods for accounting for estimation variation. One method uses a random-coefficient model, which requires all functions to be fitted with the same basis functions. An alternative method removes the same-basis restriction by means of a hierarchical Gaussian process model. In a small simulation study the hierarchical Gaussian process model outperformed the randomcoefficient model and greatly reduced the bias in the estimated first eigenvalue that would result from ignoring estimation variability. For the neuronal data the hierarchical Gaussian process estimate of the first eigenvalue was much smaller than the naive estimate that ignored variability due to function estimation. The neuronal setting also illustrates the benefit of incorporating alignment parameters into the hierarchical scheme. Copyright 2005, Oxford University Press.

Suggested Citation

  • Sam Behseta & Robert E. Kass & Garrick L. Wallstrom, 2005. "Hierarchical models for assessing variability among functions," Biometrika, Biometrika Trust, vol. 92(2), pages 419-434, June.
  • Handle: RePEc:oup:biomet:v:92:y:2005:i:2:p:419-434

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    References listed on IDEAS

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    Cited by:

    1. van der Linde, Angelika, 2008. "Variational Bayesian functional PCA," Computational Statistics & Data Analysis, Elsevier, vol. 53(2), pages 517-533, December.
    2. Angelika Linde, 2009. "A Bayesian latent variable approach to functional principal components analysis with binary and count data," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 93(3), pages 307-333, September.
    3. Silvia Montagna & Surya T. Tokdar & Brian Neelon & David B. Dunson, 2012. "Bayesian Latent Factor Regression for Functional and Longitudinal Data," Biometrics, The International Biometric Society, vol. 68(4), pages 1064-1073, December.
    4. Athanasios Kottas & Sam Behseta, 2010. "Bayesian Nonparametric Modeling for Comparison of Single-Neuron Firing Intensities," Biometrics, The International Biometric Society, vol. 66(1), pages 277-286, March.
    5. Botts, Carsten H. & Daniels, Michael J., 2008. "A flexible approach to Bayesian multiple curve fitting," Computational Statistics & Data Analysis, Elsevier, vol. 52(12), pages 5100-5120, August.

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