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A flexible approach to Bayesian multiple curve fitting

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  • Botts, Carsten H.
  • Daniels, Michael J.

Abstract

We model sparse functional data from multiple subjects with a mixed-effects regression spline. In this model, the expected values for any subject (conditioned on the random effects) can be written as the sum of a population curve and a subject-specific deviate from this population curve. The population curve and the subject-specific deviates are both modeled as free-knot b-splines with k and k' knots located at and , respectively. To identify the number and location of the "free" knots, we sample from the posterior using reversible jump MCMC methods. Sampling from this posterior distribution is complicated, however, by the flexibility we allow for the model's covariance structure. No restrictions (other than positive definiteness) are placed on the covariance parameters [psi] and [sigma]2 and, as a result, no analytical form for the likelihood exists. In this paper, we consider two approximations to and then sample from the corresponding approximations to . We also sample from which has a likelihood that is available in closed form. While sampling from this larger posterior is less efficient, the resulting marginal distribution of knots is exact and allows us to evaluate the accuracy of each approximation. We then consider a real data set and explore the difference between and the more accurate approximation to .

Suggested Citation

  • 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.
    • Handle: RePEc:eee:csdana:v:52:y:2008:i:12:p:5100-5120
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    References listed on IDEAS

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    1. Jamie L. Bigelow & David B. Dunson, 2007. "Bayesian Adaptive Regression Splines for Hierarchical Data," Biometrics, The International Biometric Society, vol. 63(3), pages 724-732, September.
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    5. Dominici F. & Daniels M. & Zeger S. L. & Samet J. M., 2002. "Air Pollution and Mortality: Estimating Regional and National Dose-Response Relationships," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 100-111, March.
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    Cited by:

    1. Dhiman Bhadra & Michael J. Daniels & Sungduk Kim & Malay Ghosh & Bhramar Mukherjee, 2012. "A Bayesian Semiparametric Approach for Incorporating Longitudinal Information on Exposure History for Inference in Case–Control Studies," Biometrics, The International Biometric Society, vol. 68(2), pages 361-370, June.
    2. Bellio, Ruggero & Grassetti, Luca, 2011. "Semiparametric stochastic frontier models for clustered data," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 71-83, January.

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