Localized Spectral Envelope

The concept of the spectral envelope was introduced as a statistical basis for the frequency domain analysis and scaling of qualitative-valued time series

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

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 flexibly 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

Does intensive management improve remission rates in patients with intermediate rheumatoid arthritis? (the TITRATE trial): study protocol for a randomised controlled trial.

BACKGROUND: Uncontrolled active rheumatoid arthritis can lead to increasing disability and reduced quality of life over time. 'Treating to target' has been shown to be effective in active established disease and also in early disease. However, there is a lack of nationally agreed treatment protocols for patients with established rheumatoid arthritis who have intermediate disease activity. This trial is designed to investigate whether intensive management of disease leads to a greater number of remissions at 12 months. Levels of disability and quality of life, and acceptability and cost-effectiveness of the intervention will also be examined. METHODS: The trial is a 12-month, pragmatic, randomised, open-label, two-arm, parallel-group, multicentre trial undertaken at specialist rheumatology centres across England. Three hundred and ninety-eight patients with established rheumatoid arthritis will be recruited. They will currently have intermediate disease activity (disease activity score for 28 joints assessed using an erythrocyte sedimentation rate of 3.2 to 5.1 with at least three active joints) and will be taking at least one disease-modifying anti-rheumatic drug. Participants will be randomly selected to receive intensive management or standard care. Intensive management will involve monthly clinical reviews with a specialist health practitioner, where drug treatment will be optimised and an individualised treatment support programme delivered based on several principles of motivational interviewing to address identified problem areas, such as pain, fatigue and adherence. Standard care will follow standard local pathways and will be in line with current English guidelines from the National Institute for Health and Clinical Excellence. Patients will be assessed initially and at 6 and 12 months through self-completed questionnaires and clinical evaluation. DISCUSSION: The trial will establish whether the known benefits of intensive treatment strategies in active rheumatoid arthritis are also seen in patients with established rheumatoid arthritis who have moderately active disease. It will evaluate both the clinical and cost-effectiveness of intensive treatment. TRIAL REGISTRATION: Current Controlled Trials, ID: ISRCTN70160382 . Registered on 16 January 2014.MRC Funding: MC_UP_1302/3 NIHR Funding: RP-PG-0610-1006

A state space approach to bootstrapping conditional forecasts in ARMA models

A bootstrap approach to evaluating conditional forecast errors in ARMA models is presented. The key to this method is the derivation of a reverse-time state space model for generating conditional data sets that capture the salient stochastic properties of the observed data series. We demonstrate the utility of the method using several simulation experiments for the MA(q) and ARMA( p, q) models. Using the state space form, we are able to investigate conditional forecast errors in these models quite easily whereas the existing literature has only addressed conditional forecast error assessment in the pure AR( p) form. Our experiments use short data sets and non-Gaussian, as well as Gaussian, disturbances. The bootstrap is found to provide useful information on error distributions in all cases and serves as a broadly applicable alternative to the asymptotic Gaussian theory

Nonparametric Frequency Detection and Optimal Coding in Molecular Biology

The concept of spectral envelope for analyzing periodicities in categorical-valued time series was introduced in the statistics literature as a computationally simple and general statistical methodology for the harmonic analysis and scaling of non-numeric sequences. One bene t of this technique is that it combines nonparametric statistical analysis with modern computer power to quickly search for diagnostic patterns within long sequences. An interesting area of application is the nucleosome positioning signals and optimal alphabets in long DNA sequences. The examples focus on period lengths in nucleosome signals and optimal alphabets in herpesviruses and we point out some inconsistencies in established gene segments

Detecting Common Signals in Multiple Time Series Using The Spectral Envelope

. The concept of the spectral envelope was recently introduced as a statistical basis for the frequency domain analysis and scaling of qualitative-valued time series. In this article we use the spectral envelope along with the notion of random frequency effects for the detection of common signals in many time series. Key words. Spectral envelope, Optimal scaling, Fourier analysis, Random frequency effects, Latent roots and vectors, Principal components, Factor Analysis, Signal detection, Functional magnetic resonance imaging (fMRI), Ambulatory blood pressure. 1 Introduction Frequently, p ? 1 time series fY j (t), t = 1; :::; n j g for j = 1; :::; p, are collected with the primary interest being whether any---and how many---have common cyclic components. The series need not be in phase and the sample lengths, n j , need not be the same, but are of the same magnitude. In this case, a common sample length, n, that is highly composite is chosen and the data are padded or shortened accord..

Automatic estimation of multivariate spectra via smoothing splines

The classical method for estimating the spectral density of a multivariate time series is first to calculate the periodogram, and then to smooth it to obtain a consistent estimator. Typically, to ensure the estimate is positive definite, all the elements of the periodogram are smoothed the same way. There are, however, many situations for which different components of the spectral matrix have different degrees of smoothness. We propose a Bayesian approach that uses Markov chain Monte Carlo techniques to fit smoothing splines to each component, real and imaginary, of the Cholesky decomposition of the periodogram matrix. The spectral estimator is then obtained by reconstructing the spectral estimator from the smoothed Cholesky decomposition components. Our technique produces an automatically smoothed spectral matrix estimator along with samples from the posterior distributions of the parameters to facilitate inference. Copyright 2007, Oxford University Press.