Automatic estimation of multivariate spectra via smoothing splines

Rosen, Ori; Stoffer, David S.

doi:10.1093/biomet/asm022

Cited by 47 publications

(48 citation statements)

References 19 publications

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“…We now take up the task of reconciling this apparent discrepancy: on the one hand, according to the basis of the nucleosome positioning code, 10bp periodicities ought be common while, on the other hand as asserted in [11], they are seldom seen. The contention that an attribute is "rarely seen" is clearly dependent on where and how the search was conducted.…”

Section: Select Dinucleotide Periodicities For High Affinity Nucleosomentioning

confidence: 99%

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Re-Cracking the Nucleosome Positioning Code

Segal

2008

Statistical Applications in Genetics and Molecular Biology

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Nucleosomes, the fundamental repeating subunits of all eukaryotic chromatin, are responsible for packaging DNA into chromosomes inside the cell nucleus and controlling gene expression. While it has been well established that nucleosomes exhibit higher affinity for select DNA sequences, until recently it was unclear whether such preferences exerted a significant, genome-wide effect on nucleosome positioning in vivo. This question was seemingly and recently resolved in the affirmative: a wide-ranging series of experimental and computational analyses provided extensive evidence that the instructions for wrapping DNA around nucleosomes are contained in the DNA itself. This subsequently labelled second genetic code was based on data-driven, structural, and biophysical considerations. It was subjected to an extensive suite of validation procedures, with one conclusion being that intrinsic, genome-encoded, nucleosome organization explains ≈50% of in vivo nucleosome positioning. Here, we revisit both the nature of the underlying sequence preferences, and the performance of the proposed code. A series of new analyses, employing spectral envelope (Fourier transform) methods for assessing key sequence periodicities, classification techniques for evaluating predictive performance, and discriminatory motif finding methods for devising alternate models, are applied. The findings from the respective analyses indicate that signature dinucleotide periodicities are absent from the bulk of the high affinity nucleosome-bound sequences, and that the predictive performance of the code is modest. We conclude that further exploration of the role of sequence-based preferences in genome-wide nucleosome positioning is warranted. This work offers a methodologic counterpart to a recent, high resolution determination of nucleosome positioning that also questions the accuracy of the proposed code and, further, provides illustration of techniques useful in assessing sequence periodicity and predictive performance.

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Section: Select Dinucleotide Periodicities For High Affinity Nucleosomentioning

confidence: 99%

“…Notably, the (Fourier-based) spectral envelope, built on work of Stoffer and colleagues [9; 10], and briefly outlined in Methods, has been employed. Accordingly, the following quote from Rosen and Stoffer [11], is of interest (emphasis added):…”

Section: Select Dinucleotide Periodicities For High Affinity Nucleosomentioning

confidence: 99%

Re-Cracking the Nucleosome Positioning Code

Segal

2008

Statistical Applications in Genetics and Molecular Biology

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“…While in the univariate setting the spectrum is smoothed on the logarithmic scale to preserve positivity, Cholesky components of spectral matrices can be smoothed to preserve positive-definiteness in the multivariate setting (Dai and Guo, 2004; Rosen and Stoffer, 2007; Krafty and Collinge, 2013). The modified Cholesky decomposition assures that, for a spectral matrix f ( ω ), there exists a unique P × P lower triangular complex matrix Θ( ω ) with ones on the diagonal and a unique P × P positive diagonal matrix Ψ ( ω ) such that…”

Section: Methodological Background: Spectral Domain Analysismentioning

confidence: 99%

“…Efficient nonparametric methods that preserve the positive-definite Hermitian structure of spectral matrices have been developed for the simpler, classical problem of estimating the power spectrum of a multivariate time series from a single subject by modeling Cholesky components of spectral matrices as functions of frequency (Dai and Guo, 2004; Rosen and Stoffer, 2007; Krafty and Collinge, 2013). In this article, we extend this framework to develop a new approach to analyzing data from multiple subjects that models Cholesky components as functions of both frequency and outcome.…”

Section: Introductionmentioning

confidence: 99%

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

Krafty

Rosen

Stoffer

et al. 2017

Journal of the American Statistical Association

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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.

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“…[8], [10], [16], [15]. In [2], [7], a new approach to scalar spectral estimation, called THREE, was introduced by Byrnes, Georgiou and Lindquist.…”

Section: Introductionmentioning

confidence: 99%

A new metric for multivariate spectral estimation leading to lowest complexity spectra

Ferrante

Masiero

Pavon

2011

IEEE Conference on Decision and Control and European Control Conference

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A new multivariate spectral estimation technique is proposed. It is based on a constrained spectrum approximation problem, where the distance between spectra is derived from the relative entropy rate between stationary Gaussian processes. This approach may be viewed as an extension of the high-resolution estimator called THREE introduced by Byrnes, Georgiou and Lindquist in 2000. The corresponding solution features a complexity upper bound which is equal to the one featured by THREE in the scalar case thereby improving on the one so far available in the multichannel framework. The solution is computed by means of a globally convergent, matricial Newton-type algorithm. Comparative simulation indicates that this new technique outperforms PEM and N4SID in the case of short data records.

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Automatic estimation of multivariate spectra via smoothing splines

Cited by 47 publications

References 19 publications

Re-Cracking the Nucleosome Positioning Code

Re-Cracking the Nucleosome Positioning Code

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

A new metric for multivariate spectral estimation leading to lowest complexity spectra

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