616 research outputs found
Spectral Density Bandwidth Choice: Source of Nonmonotonic Power for Tests of a Mean Shift in a Time Series
Data dependent bandwidth choices for zero frequency spectral density estimators of a time series are shown to be an important source of nonmonotonic power when testing for a shift in mean. It is shown that if the spectral density is estimated under the null hypothesis of a stable mean using a data dependent bandwidth (with or without prewhitening), non-monotonic power appears naturally for some popular tests including the CUSUM test. On the other hand, under some fixed bandwidth choices, power is monotonic. Empirical examples and simulations illustrate these power properties. Theoretical explanations for the power results are provided.
Longitudinal Scalar-on-Function Regression with Application to Tractography Data
We propose a class of estimation techniques for scalar-on-function regression in longitudinal studies where both outcomes, such as test results on motor functions, and functional predictors, such as brain images, may be observed at multiple visits. Our methods are motivated by a longitudinal brain diffusion tensor imaging (DTI) tractography study. One of the primary goals of the study is to evaluate the contemporaneous association between human function and brain imaging over time. The complexity of the study requires development of methods that can simultaneously incorporate: (1) multiple functional (and scalar) regressors; (2) longitudinal outcome and functional predictors measurements per patient; (3) Gaussian or non-Gaussian outcomes; and, (4) missing values within functional predictors. We review existing approaches designed to handle such types of data and discuss their limitations. We propose two versions of a new method, longitudinal functional principal components regression. These methods extend the well-known functional principal component regression and allow for different effects of subject-specific trends in curves and of visit-specific deviations from that trend. The different methods are compared in simulation studies, and the most promising approaches are used for analyzing the tractography data
Fast Covariance Estimation for High-dimensional Functional Data
For smoothing covariance functions, we propose two fast algorithms that scale
linearly with the number of observations per function. Most available methods
and software cannot smooth covariance matrices of dimension with
; the recently introduced sandwich smoother is an exception, but it is
not adapted to smooth covariance matrices of large dimensions such as . Covariance matrices of order , and even , are
becoming increasingly common, e.g., in 2- and 3-dimensional medical imaging and
high-density wearable sensor data. We introduce two new algorithms that can
handle very large covariance matrices: 1) FACE: a fast implementation of the
sandwich smoother and 2) SVDS: a two-step procedure that first applies singular
value decomposition to the data matrix and then smoothes the eigenvectors.
Compared to existing techniques, these new algorithms are at least an order of
magnitude faster in high dimensions and drastically reduce memory requirements.
The new algorithms provide instantaneous (few seconds) smoothing for matrices
of dimension and very fast ( 10 minutes) smoothing for
. Although SVDS is simpler than FACE, we provide ready to use,
scalable R software for FACE. When incorporated into R package {\it refund},
FACE improves the speed of penalized functional regression by an order of
magnitude, even for data of normal size (). We recommend that FACE be
used in practice for the analysis of noisy and high-dimensional functional
data.Comment: 35 pages, 4 figure
Bayesian Functional Data Analysis Using WinBUGS
We provide user friendly software for Bayesian analysis of functional data models using \pkg{WinBUGS}~1.4. The excellent properties of Bayesian analysis in this context are due to: (1) dimensionality reduction, which leads to low dimensional projection bases; (2) mixed model representation of functional models, which provides a modular approach to model extension; and (3) orthogonality of the principal component bases, which contributes to excellent chain convergence and mixing properties. Our paper provides one more, essential, reason for using Bayesian analysis for functional models: the existence of software.
Bayesian Analysis for Penalized Spline Regression Using WinBUGS
Penalized splines can be viewed as BLUPs in a mixed model framework, which allows the use of mixed model software for smoothing. Thus, software originally developed for Bayesian analysis of mixed models can be used for penalized spline regression. Bayesian inference for nonparametric models enjoys the flexibility of nonparametric models and the exact inference provided by the Bayesian inferential machinery. This paper provides a simple, yet comprehensive, set of programs for the implementation of nonparametric Bayesian analysis in WinBUGS. Good mixing properties of the MCMC chains are obtained by using low-rank thin-plate splines, while simulation times per iteration are reduced employing WinBUGS specific computational tricks.
Proofs of theorems for the JRSS-B paper `Likelihood ratio tests in linear mixed models with one variance component'
Proofs of theorems for the JRSS-B paper `Likelihood ratio tests in linear mixed models with one variance component
Multilevel functional principal component analysis
The Sleep Heart Health Study (SHHS) is a comprehensive landmark study of
sleep and its impacts on health outcomes. A primary metric of the SHHS is the
in-home polysomnogram, which includes two electroencephalographic (EEG)
channels for each subject, at two visits. The volume and importance of this
data presents enormous challenges for analysis. To address these challenges, we
introduce multilevel functional principal component analysis (MFPCA), a novel
statistical methodology designed to extract core intra- and inter-subject
geometric components of multilevel functional data. Though motivated by the
SHHS, the proposed methodology is generally applicable, with potential
relevance to many modern scientific studies of hierarchical or longitudinal
functional outcomes. Notably, using MFPCA, we identify and quantify
associations between EEG activity during sleep and adverse cardiovascular
outcomes.Comment: Published in at http://dx.doi.org/10.1214/08-AOAS206 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Nonlinear tube-fitting for the analysis of anatomical and functional structures
We are concerned with the estimation of the exterior surface and interior
summaries of tube-shaped anatomical structures. This interest is motivated by
two distinct scientific goals, one dealing with the distribution of HIV
microbicide in the colon and the other with measuring degradation in
white-matter tracts in the brain. Our problem is posed as the estimation of the
support of a distribution in three dimensions from a sample from that
distribution, possibly measured with error. We propose a novel tube-fitting
algorithm to construct such estimators. Further, we conduct a simulation study
to aid in the choice of a key parameter of the algorithm, and we test our
algorithm with validation study tailored to the motivating data sets. Finally,
we apply the tube-fitting algorithm to a colon image produced by single photon
emission computed tomography (SPECT) and to a white-matter tract image produced
using diffusion tensor imaging (DTI).Comment: Published in at http://dx.doi.org/10.1214/10-AOAS384 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Soft Null Hypotheses: A Case Study of Image Enhancement Detection in Brain Lesions
This work is motivated by a study of a population of multiple sclerosis (MS)
patients using dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI)
to identify active brain lesions. At each visit, a contrast agent is
administered intravenously to a subject and a series of images is acquired to
reveal the location and activity of MS lesions within the brain. Our goal is to
identify and quantify lesion enhancement location at the subject level and
lesion enhancement patterns at the population level. With this example, we aim
to address the difficult problem of transforming a qualitative scientific null
hypothesis, such as "this voxel does not enhance", to a well-defined and
numerically testable null hypothesis based on existing data. We call the
procedure "soft null hypothesis" testing as opposed to the standard "hard null
hypothesis" testing. This problem is fundamentally different from: 1) testing
when a quantitative null hypothesis is given; 2) clustering using a mixture
distribution; or 3) identifying a reasonable threshold with a parametric null
assumption. We analyze a total of 20 subjects scanned at 63 visits (~30Gb), the
largest population of such clinical brain images
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