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Bayesian Analysis of Curves Shape Variation Through Registration and Regression

  • Chapter
Nonparametric Bayesian Inference in Biostatistics

Part of the book series: Frontiers in Probability and the Statistical Sciences ((FROPROSTAS))

Abstract

Misalignment of functional features in a sample of random curves leads to potentially misleading inference, when variation in timing is ignored. This chapter reviews the use of Bayesian hierarchical curve registration in Biostatistics and Bioinformatics. Several models allowing for unit-specific random time scales are discussed and applied to longitudinal data arising in biomedicine, pharmacokinetics, and time-course genomics. We consider representations of random functionals based on P-spline priors. Under this framework, straightforward posterior simulation strategies are outlined for inference. Beyond curve registration, we discuss joint regression modeling of both random effects and population level functional quantities. Finally, the use of mixture priors is discussed in the setting of differential expression analysis.

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Notes

  1. 1.

    In our development, X ∼ Ga(a; b) is parametrized so that \(E[X] = a/b\).

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Author information

Authors and Affiliations

  1. University of California Los Angeles, Los Angeles, CA, USA

    Donatello Telesca

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  1. Donatello Telesca
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Correspondence to Donatello Telesca .

Editor information

Editors and Affiliations

  1. Department of Bioinformatics and Biostatistics, University of Louisville, Louisville, Kentucky, USA

    Riten Mitra

  2. Department of Mathematics, University of Texas, Austin, Texas, USA

    Peter Müller

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Telesca, D. (2015). Bayesian Analysis of Curves Shape Variation Through Registration and Regression. In: Mitra, R., Müller, P. (eds) Nonparametric Bayesian Inference in Biostatistics. Frontiers in Probability and the Statistical Sciences. Springer, Cham. https://doi.org/10.1007/978-3-319-19518-6_14

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