Bayesian Hierarchical Curve Registration

Functional data often exhibit a common shape, but with variations in amplitude and phase across curves. The analysis often proceeds by synchronization of the data through curve registration. In this article we propose a Bayesian hierarchical model for curve registration. Our hierarchical model provides a formal account of amplitude and phase variability while borrowing strength from the data across curves in the estimation of the model parameters. We discuss extensions of the model by using penalized B-splines in the representation of the shape and time-transformation functions, and by allowing temporal misalignment of the curves. We discuss applications of our model to simulated data, as well as to two data sets. In particular, we use our model in a nonstandard analysis aimed at investigating regulatory network in time course microarray data.

[1]  R. D. Tuddenham,et al.  Physical growth of California boys and girls from birth to eighteen years. , 1954, Publications in child development. University of California, Berkeley.

[2]  E. A. Sylvestre,et al.  Self Modeling Nonlinear Regression , 1972 .

[3]  S. Chiba,et al.  Dynamic programming algorithm optimization for spoken word recognition , 1978 .

[4]  C. R. Deboor,et al.  A practical guide to splines , 1978 .

[5]  T. Gasser,et al.  Convergence and consistency results for self-modeling nonlinear regression , 1988 .

[6]  W. Härdle.  Applied Nonparametric Regression , 1991 .

[7]  T. Gasser,et al.  Statistical Tools to Analyze Data Representing a Sample of Curves , 1992 .

[8]  W. Härdle.  Applied Nonparametric Regression , 1992 .

[9]  T. Gasser,et al.  Searching for Structure in Curve Samples , 1995 .

[10]  Bernard W. Silverman,et al.  Incorporating parametric effects into functional principal components analysis , 1995 .

[11]  R D Bock,et al.  Comparison of height acceleration curves in the Fels, Zurich, and Berkeley growth data. , 1995, Annals of human biology.

[12]  Random Time Transformations , 1997 .

[13]  T. Gasser,et al.  Alignment of curves by dynamic time warping , 1997 .

[14]  Michael Ruogu Zhang,et al.  Comprehensive identification of cell cycle-regulated genes of the yeast Saccharomyces cerevisiae by microarray hybridization. , 1998, Molecular biology of the cell.

[15]  J. Ramsay,et al.  Curve registration , 2018, Oxford Handbooks Online.

[16]  T. Gasser,et al.  Synchronizing sample curves nonparametrically , 1999 .

[17]  J. Ramsay,et al.  Curve registration by local regression , 2000 .

[18]  Michal Linial,et al.  Using Bayesian Networks to Analyze Expression Data , 2000, J. Comput. Biol..

[19]  Birgitte B. Rønn,et al.  Nonparametric maximum likelihood estimation for shifted curves , 2001 .

[20]  B. Silverman,et al.  Functional Data Analysis , 1997 .

[21]  M. Gerstein,et al.  Beyond synexpression relationships: local clustering of time-shifted and inverted gene expression profiles identifies new, biologically relevant interactions. , 2001, Journal of molecular biology.

[22]  James O. Ramsay,et al.  Applied Functional Data Analysis: Methods and Case Studies , 2002 .

[23]  Brian J. Smith,et al.  BAYESIAN OUTPUT ANALYSIS PROGRAM (BOA) VERSION 1.1 USER'S MANUAL , 2003 .

[24]  M. Gerstein,et al.  Genomic analysis of gene expression relationships in transcriptional regulatory networks. , 2003, Trends in genetics : TIG.

[25]  T. Gasser,et al.  Self‐modelling warping functions , 2004 .

[26]  Ciprian M. Crainiceanu,et al.  Spatially Adaptive Bayesian P-Splines with Heteroscedastic Errors , 2004 .

[27]  D. Ruppert.  The Elements of Statistical Learning: Data Mining, Inference, and Prediction , 2004 .

[28]  Mary J Lindstrom,et al.  Self Modeling with Flexible, Random Time Transformations , 2004, Biometrics.

[29]  S. Lang,et al.  Bayesian P-Splines , 2004 .

[30]  H. Müller,et al.  Functional Convex Averaging and Synchronization for Time-Warped Random Curves , 2004 .

[31]  Lurdes Y T Inoue,et al.  Cluster-based network model for time-course gene expression data. , 2007, Biostatistics.

[32]  S. E. Ahmed,et al.  Markov Chain Monte Carlo: Stochastic Simulation for Bayesian Inference , 2008, Technometrics.

[33]  Olivier Meste,et al.  Core Shape modelling of a set of curves , 2010, Comput. Stat. Data Anal..