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Krafty RT, Rosen O, Stoffer DS, et al. Conditional Spectral Analysis of Replicated Multiple Time Series with Application to Nocturnal Physiology. J Am Stat Assoc. 2017;112(520):1405-1416doi: 10.1080/01621459.2017.1281811.
Krafty, R. T., Rosen, O., Stoffer, D. S., Buysse, D. J., & Hall, M. H. (2017). Conditional Spectral Analysis of Replicated Multiple Time Series with Application to Nocturnal Physiology. Journal of the American Statistical Association, 112(520), 1405-1416. https://doi.org/10.1080/01621459.2017.1281811
Krafty, Robert T, et al. "Conditional Spectral Analysis of Replicated Multiple Time Series with Application to Nocturnal Physiology." Journal of the American Statistical Association vol. 112,520 (2017): 1405-1416. doi: https://doi.org/10.1080/01621459.2017.1281811
Krafty RT, Rosen O, Stoffer DS, Buysse DJ, Hall MH. Conditional Spectral Analysis of Replicated Multiple Time Series with Application to Nocturnal Physiology. J Am Stat Assoc. 2017;112(520):1405-1416. doi: 10.1080/01621459.2017.1281811. Epub 2017 Jan 20. PMID: 29430069; PMCID: PMC5805231.
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J Am Stat Assoc. 2017;112(520):1405-1416. doi: 10.1080/01621459.2017.1281811. Epub 2017 Jan 20.

Conditional Spectral Analysis of Replicated Multiple Time Series with Application to Nocturnal Physiology.

Journal of the American Statistical Association

Robert T Krafty, Ori Rosen, David S Stoffer, Daniel J Buysse, Martica H Hall

Affiliations

  1. Associate Professor, Department of Biostatistics, University of Pittsburgh.
  2. Professor, Department of Mathematical Sciences, University of Texas at El Paso.
  3. Professor, Department of Statistics, University of Pittsburgh.
  4. Professor, Department of Psychiatry, University of Pittsburgh.

PMID: 29430069 PMCID: PMC5805231 DOI: 10.1080/01621459.2017.1281811

Abstract

This article considers the problem of analyzing associations between power spectra of multiple time series and cross-sectional outcomes when data are observed from multiple subjects. The motivating application comes from sleep medicine, where researchers are able to non-invasively record physiological time series signals during sleep. The frequency patterns of these signals, which can be quantified through the power spectrum, contain interpretable information about biological processes. An important problem in sleep research is drawing connections between power spectra of time series signals and clinical characteristics; these connections are key to understanding biological pathways through which sleep affects, and can be treated to improve, health. Such analyses are challenging as they must overcome the complicated structure of a power spectrum from multiple time series as a complex positive-definite matrix-valued function. This article proposes a new approach to such analyses based on a tensor-product spline model of Cholesky components of outcome-dependent power spectra. The approach exibly models power spectra as nonparametric functions of frequency and outcome while preserving geometric constraints. Formulated in a fully Bayesian framework, a Whittle likelihood based Markov chain Monte Carlo (MCMC) algorithm is developed for automated model fitting and for conducting inference on associations between outcomes and spectral measures. The method is used to analyze data from a study of sleep in older adults and uncovers new insights into how stress and arousal are connected to the amount of time one spends in bed.

Keywords: Bayesian Analysis; Coherence; Heart Rate Variability; MCMC; Multivariate Time Series; Sleep; Smoothing Spline; Spectral Analysis; Tensor-Product ANOVA; Whittle Likelihood

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