Detecting and Localizing Differences in Functional Time Series Dynamics: A Case Study in Molecular Biophysics
成果类型：
Article
署名作者：
Tavakoli, Shahin; Panaretos, Victor M.
署名单位：
University of Cambridge; Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne
刊物名称：
JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
ISSN/ISSBN：
0162-1459
DOI：
10.1080/01621459.2016.1147355
发表日期：
2016
页码：
1020-1035
关键词：
false discovery rate
covariance operators
principal-components
dna
simulations
inference
EQUALITY
distributions
INDEPENDENCE
stationarity
摘要：
Motivated by the problem of inferring the molecular dynamics of DNA in solution, and linking them with its base-pair composition, we consider the problem of comparing the dynamics of functional time series (FTS), and of localizing any inferred differences in frequency and along curvelength. The approath we take is one of Fourier analysis, where the complete second-order structure of the FTS is encoded by its spectral density operator, indexed by frequency and curvelength. The comparison is broken down to a hierarchy of stages: at a global level, we compare the spectral density operators of the two FTS, across frequencies and curve length, based on a Hilbert-Schmidt criterion; then, we localize any differences to specific frequencies; and, finally, we further localize any differences along the length of the random curves, that is, in physical space. A hierarchical multiple testing approach guarantees control of the averaged false discovery rate over the selected frequencies. In this sense, we are able to attribute any differences to distinct dynamic (frequency) and spatial (curvelength) contributions. Our approach is presented and illustrated by means of a case study in molecular biophysics: how can one use-molecular dynamics simulations of short strands of DNA to infer their temporal dynamics at the scaling limit, and probe whether these depend on the sequence encoded in these strands? Supplementary materials for this article are available online.