Costa, M. J., Finkenstädt, Bärbel, Gould, Peter D., Foreman, Julia, Halliday, Karen J., Hall, Anthony J. W. and Rand, D. A. (David A.) (2011) Estimating periodicity of oscillatory time series through resampling techniques. Working Paper. University of Warwick. Centre for Research in Statistical Methodology, Coventry.

Preview

PDF WRAP_Costa_11-1w.pdf - Published Version - Requires a PDF viewer such as GSview, Xpdf or Adobe Acrobat Reader Download (492Kb)

Abstract

Accurate estimation of the period length of time-course data from cyclical biological processes, such as those driven by the endogenous circadian pacemaker, is crucial for making inferences about the properties of the biological clock found in many living organisms. In this paper we propose a methodology that combines spectral analysis with resampling techniques termed spectrum resampling (SR). Extensive numerical studies show that SR is superior and considerably more robust to non-sinusoidal patterns than currently available methods based on Fourier approximations, namely the FFT-NLLS method by Plautz et al. (1997, Journal of Biological Rhythms 12, 204-217). We also develop a nonparametric test for testing for changes in period length. The test uses resampling techniques and allows for period estimates with different variances. Simulation studies show that it attains correct nominal size and has good power properties when compared to parametric alternatives. The proposed SR method and statistical test are illustrated with real data examples.

Item Type:	Working or Discussion Paper (Working Paper)
Subjects:	Q Science > QA Mathematics Q Science > QP Physiology
Divisions:	Faculty of Science > Statistics Faculty of Science > Centre for Systems Biology
Library of Congress Subject Headings (LCSH):	Circadian rhythms -- Mathematical models, Spectrum analysis, Resampling (Statistics)
Series Name:	Working papers
Publisher:	University of Warwick. Centre for Research in Statistical Methodology
Place of Publication:	Coventry
Date:	2011
Volume:	Vol.2011
Number:	No.1
Status:	Not Peer Reviewed
Access rights to Published version:	Open Access
Funder:	Engineering and Physical Sciences Research Council (EPSRC), Biotechnology and Biological Sciences Research Council (Great Britain) (BBSRC), European Union (EU)
Grant number:	BB/F005261/1 (BBSRC), BB/F005237/1 (BBSRC), BB/F005318/1 (BBSRC), EP/C544587/1 (EPSRC), 005137 (EU)
References:	Brillinger, D. R. (2001). Time Series: Data Analysis and Theory. Classics in Applied Mathematics. SIAM. Burg, J. P. (1972). The relationship between maximum entropy spectra and maximum likelihood spectra. Geophysics 37, 375{376. Carpenter, J. and Bithell, J. (2000). Bootstrap confidence intervals: when, which, what? A practical guide for medical statisticians. Statistics in Medicine 19, 1141{1164. Chatfield, C. (2003). The Analysis of Time Series: An Introduction. Chapman & Hall/CRC. Dahlhaus, R. and Janas, D. (1996). A frequency domain bootstrap for ratio statistics in time series analysis. The Annals of Statistics 24, 1934{1963. Davidson, A. C. and Hinkley, D. V. (1997). Bootstrap Methods and their Application. Cambridge University Press. Davidson, R. and MacKinnon, J. G. (1998). Graphical methods for investigating the size and power of hypothesis tests. The Manchester School 66, 1{26. Davidson, R. and MacKinnon, J. G. (2000). Bootstrap tests: how many bootstraps ? Econometrics Review 19, 55{68. Dowse, H. B. and Ringo, J. M. (1989). The search for hidden periodicities in biological time series revisited. Journal of Theoretical Biology 139, 487{515. Dowse, H. B. and Ringo, J. M. (1991). Comparisons between periodograms and spectral analysis: apples are apples after all. Journal of Theoretical Biology 148, 139{144. Edwards, K. D., Anderson, P. E., Hall, A., Salathia, N. S., Locke, J. C., Lynn, J. R., Straume, M., Smith, J. Q., and Millar, A. J. (2006). FLOWERING LOCUS C mediates natural variation in the high-temperature response of the Arabidopsis circadian clock. The Plant Cell 18, 639{650. Efron, B. (1979). Bootstrap methods: Another look at the jackknife. The Annals of Statistics 7, 1{26. Franke, J. and Hardle, W. (1992). On bootstrapping kernel spectral estimates. The Annals of Statistics 20, 121{145. Goldberg, L. R., Kercheval, A. N., and Lee, K. (2005). t-Statistics for weighted means in credit risk modelling. Journal of Risk Finance 6, 349{365. Goldbeter, A. (1991). A minimal cascade model for the mitotic oscillator involving cyclin and cdc2 kinase. Proceedings of the National Academy of Sciences 88, 9107{9111. Hall, A., Bastow, R. M., Davis, S. J., Hanano, S., McWatters, H. G., Hibberd, V., Doyle, M. R., Sung, S., Halliday, K. J., Amasino, R. M., and Millar, A. J. (2003). The TIME FOR COFFEE gene maintains the amplitude and timing of Arabidopsis circadian clocks. The Plant Cell 15, 2719{2729. Hardle, W. and Bowman, A. W. (1988). Bootstrapping in nonparametric regression: Local adaptive smoothing and confidence bands. Journal of the American Statistical Association 83, 102{110. Harris, F. J. (1997). On the use of windows for harmonic analysis with the discrete Fourier transform. Biometrika 84, 965{969. Heron, E. A., Finkenstadt, B., and Rand, D. A. (2007). Bayesian inference for dynamic transcriptional regulation: the hes1 system as a case study. Bioinformatics 23, 2589{2595. James, A. B., Monreal, J. A., Nimmo, G. A., Kelly, C. L., Herzyk, P., Jenkins, G. I., and Nimmo, H. G. (2008). The circadian clock in Arabidopsis roots is a simplified slave version of the clock in shoots. Science 322, 1832{1835. Jenkins, G. M. and Watts, D. G. (1968). Spectral Analysis and Its Applications. Holden-Day. Jensen, M. H., Sneppen, K., and Tiana, G. (2003). Sustained oscillations and time delays in gene expression of protein Hes1. FEBS Letters 541, 176{177. Kreiss, J.-P. and Paparoditis, E. (2003). Autoregressive-aided periodogram bootstrap for time series. The Annals of Statistics 31, 1923{1955. Krishnan, B., Levine, J. D., Lynch, M. K. S., Dowse, H. B., Funes, P., Hall, J. C., Hardin, P. E., and Dryer, S. E. (2001). A new role for cryptochrome in a Drosophila circadian oscillator. Nature 411, 313{317. Lee, T. C. (1997). A simple span selector for periodogram smoothing. Biometrika 84, 965{969. Marple, L. (1980). A new autoregressive spectrum analysis algorithm. IEEE Transactions on Acoustics, Speech, and Signal Processing 28, 441{454. Monk, N. A. M. (2003). Oscillatory expression of Hes1, p53, and NF-kB driven by transcriptional time delays. Current Biology 13, 1409{1413. Paparoditis, E. (2002). Frequency Domain Bootstrap for Time Series, chapter VI, pages 365{381. Empirical Process Techniques for Dependent Data. Birkhauser. Paparoditis, E. and Politis, D. N. (2003). The local bootstrap for periodogram statistics. Journal of Time Series Analysis 20, 193{222. Parzen, E. (1962). On estimation of a probability density function and mode. The Annals of Mathematical Statistics 33, 1065{1076. Plautz, J. D., Straume, M., Stanewsky, R., Jamison, C. F., Brandes, C., Dowse, H. B., Hall, J. C., and Kay, S. A. (1997). Quantitative analysis of drosophila period gene transcription in living animals. Journal of Biological Rhythms 12, 204{217. Price, T. S., Baggs, J. E., Curtis, A. M., FitzGerald, G. A., and Hogenesch, J. B. (2008). WAVECLOCK: wavelet analysis of circadian oscillation. Bioinformatics 24, 2794{2795. Roenneberg, T., Chua, E. J., Bernardo, R., and Mendoza, E. (2008). Modelling biological rhythms. Current Biology 18, 826{835. Satterthwaite, F. E. (1946). An approximate distribution of estimates of variance components. Biometrics Bulletin 2, 110{114. Sergides, M. and Paparoditis, E. (2007). Bootstrapping the local periodogram of locally stationary processes. Journal of Time Series Analysis 29, 264{299. Stoica, P. and Sundin, T. (1999). Optimally smoothed periodogram. Signal Processing 78, 253{264. Straume, M., Frasier-Cadoret, S. G., and Johnson, M. L. (1991). Least Squares Analysis of Fluorescence Data, chapter 4, pages 117{240. Topics in Fluorescence Spectroscopy, Volume 2: Principles. Plenum, New York. Welch, B. L. (1947). The generalization of Student's problem when several different population variances are involved. Biometrika 34, 28{35. Zoubir, A. M. (2010). Bootstrapping spectra: Methods, comparisons and application to knock data. Signal Processing 90, 1424{1435.
URI:	http://wrap.warwick.ac.uk/id/eprint/34870

Request changes to a record

Actions (login required)

View Item