title: Robust detection of periodic time series measured from biological systems.
abstract: BACKGROUND
  Periodic phenomena are widespread in biology. The problem of finding periodicity in biological time series can be viewed as a multiple hypothesis testing of the spectral content of a given time series. The exact noise characteristics are unknown in many bioinformatics applications. Furthermore, the observed time series can exhibit other non-idealities, such as outliers, short length and distortion from the original wave form. Hence, the computational methods should preferably be robust against such anomalies in the data.
  
  
  RESULTS
  We propose a general-purpose robust testing procedure for finding periodic sequences in multiple time series data. The proposed method is based on a robust spectral estimator which is incorporated into the hypothesis testing framework using a so-called g-statistic together with correction for multiple testing. This results in a robust testing procedure which is insensitive to heavy contamination of outliers, missing-values, short time series, nonlinear distortions, and is completely insensitive to any monotone nonlinear distortions. The performance of the methods is evaluated by performing extensive simulations. In addition, we compare the proposed method with another recent statistical signal detection estimator that uses Fisher's test, based on the Gaussian noise assumption. The results demonstrate that the proposed robust method provides remarkably better robustness properties. Moreover, the performance of the proposed method is preferable also in the standard Gaussian case. We validate the performance of the proposed method on real data on which the method performs very favorably.
  
  
  CONCLUSIONS
  As the time series measured from biological systems are usually short and prone to contain different kinds of non-idealities, we are very optimistic about the multitude of possible applications for our proposed robust statistical periodicity detection method.
authors.affiliation: Institute of Signal Processing, Tampere University of Technology, P.O. Box 553, 33101 Tampere, Finland. miika.ahdesmaki@tut.fi
authors.forename: Miika
authors.initials: M
authors.lastname: Ahdesmäki
authors.forename: Harri
authors.initials: H
authors.lastname: Lähdesmäki
authors.forename: Ron
authors.initials: R
authors.lastname: Pearson
authors.forename: Heikki
authors.initials: H
authors.lastname: Huttunen
authors.forename: Olli
authors.initials: O
authors.lastname: Yli-Harja
mesh_terms: D000465:Algorithms; D000818:Animals; D016000:Cluster Analysis; D019295:Computational Biology / Q000379:methods*; D003198:Computer Simulation; D003627:Data Interpretation, Statistical; D020869:Gene Expression Profiling; D006801:Humans; D016013:Likelihood Functions; D008954:Models, Biological; D015233:Models, Statistical; D016571:Neural Networks, Computer; D016011:Normal Distribution; D020411:Oligonucleotide Array Sequence Analysis; D018401:Sample Size; D012984:Software; D018709:Statistics, Nonparametric; D013997:Time Factors