3,571 research outputs found
Topological inference for EEG and MEG
Neuroimaging produces data that are continuous in one or more dimensions.
This calls for an inference framework that can handle data that approximate
functions of space, for example, anatomical images, time--frequency maps and
distributed source reconstructions of electromagnetic recordings over time.
Statistical parametric mapping (SPM) is the standard framework for whole-brain
inference in neuroimaging: SPM uses random field theory to furnish -values
that are adjusted to control family-wise error or false discovery rates, when
making topological inferences over large volumes of space. Random field theory
regards data as realizations of a continuous process in one or more dimensions.
This contrasts with classical approaches like the Bonferroni correction, which
consider images as collections of discrete samples with no continuity
properties (i.e., the probabilistic behavior at one point in the image does not
depend on other points). Here, we illustrate how random field theory can be
applied to data that vary as a function of time, space or frequency. We
emphasize how topological inference of this sort is invariant to the geometry
of the manifolds on which data are sampled. This is particularly useful in
electromagnetic studies that often deal with very smooth data on scalp or
cortical meshes. This application illustrates the versatility and simplicity of
random field theory and the seminal contributions of Keith Worsley
(1951--2009), a key architect of topological inference.Comment: Published in at http://dx.doi.org/10.1214/10-AOAS337 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Multiple testing of local maxima for detection of peaks in 1D
A topological multiple testing scheme for one-dimensional domains is proposed
where, rather than testing every spatial or temporal location for the presence
of a signal, tests are performed only at the local maxima of the smoothed
observed sequence. Assuming unimodal true peaks with finite support and
Gaussian stationary ergodic noise, it is shown that the algorithm with
Bonferroni or Benjamini--Hochberg correction provides asymptotic strong control
of the family wise error rate and false discovery rate, and is power
consistent, as the search space and the signal strength get large, where the
search space may grow exponentially faster than the signal strength.
Simulations show that error levels are maintained for nonasymptotic conditions,
and that power is maximized when the smoothing kernel is close in shape and
bandwidth to the signal peaks, akin to the matched filter theorem in signal
processing. The methods are illustrated in an analysis of electrical recordings
of neuronal cell activity.Comment: Published in at http://dx.doi.org/10.1214/11-AOS943 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Evaluation of second-level inference in fMRI analysis
We investigate the impact of decisions in the second-level (i.e., over subjects) inferential process in functional magnetic resonance imaging on (1) the balance between false positives and false negatives and on (2) the data-analytical stability, both proxies for the reproducibility of results. Second-level analysis based on a mass univariate approach typically consists of 3 phases. First, one proceeds via a general linear model for a test image that consists of pooled information from different subjects. We evaluate models that take into account first-level (within-subjects) variability and models that do not take into account this variability. Second, one proceeds via inference based on parametrical assumptions or via permutation-based inference. Third, we evaluate 3 commonly used procedures to address the multiple testing problem: familywise error rate correction, False Discovery Rate (FDR) correction, and a two-step procedure with minimal cluster size. Based on a simulation study and real data we find that the two-step procedure with minimal cluster size results in most stable results, followed by the familywise error rate correction. The FDR results in most variable results, for both permutation-based inference and parametrical inference. Modeling the subject-specific variability yields a better balance between false positives and false negatives when using parametric inference
Multiple Testing of Local Maxima for Detection of Peaks in Random Fields
A topological multiple testing scheme is presented for detecting peaks in
images under stationary ergodic Gaussian noise, where tests are performed at
local maxima of the smoothed observed signals. The procedure generalizes the
one-dimensional scheme of Schwartzman et al. (2011) to Euclidean domains of
arbitrary dimension. Two methods are developed according to two different ways
of computing p-values: (i) using the exact distribution of the height of local
maxima (Cheng and Schwartzman, 2014), available explicitly when the noise field
is isotropic; (ii) using an approximation to the overshoot distribution of
local maxima above a pre-threshold (Cheng and Schwartzman, 2014), applicable
when the exact distribution is unknown, such as when the stationary noise field
is non-isotropic. The algorithms, combined with the Benjamini-Hochberg
procedure for thresholding p-values, provide asymptotic strong control of the
False Discovery Rate (FDR) and power consistency, with specific rates, as the
search space and signal strength get large. The optimal smoothing bandwidth and
optimal pre-threshold are obtained to achieve maximum power. Simulations show
that FDR levels are maintained in non-asymptotic conditions. The methods are
illustrated in a nanoscopy image analysis problem of detecting fluorescent
molecules against the image background.Comment: 30 pages, 5 figures. arXiv admin note: text overlap with
arXiv:1203.306
Statistical inference in brain graphs using threshold-free network-based statistics
The description of brain networks as graphs where nodes represent different brain regions and edges represent a measure of connectivity between a pair of nodes is an increasingly used approach in neuroimaging research. The development of powerful methods for edge-wise grouplevel statistical inference in brain graphs while controlling for multiple-testing associated falsepositive rates, however, remains a difficult task. In this study, we use simulated data to assess the properties of threshold-free network-based statistics (TFNBS). The TFNBS combines thresholdfree cluster enhancement, a method commonly used in voxel-wise statistical inference, and network-based statistic (NBS), which is frequently used for statistical analysis of brain graphs. Unlike the NBS, TFNBS generates edge-wise significance values and does not require the a priori definition of a hard cluster-defining threshold. Other test parameters, nonetheless, need to be set. We show that it is possible to find parameters that make TFNBS sensitive to strong and topologically clustered effects, while appropriately controlling false-positive rates. Our results show that the TFNBS is an adequate technique for the statistical assessment of brain graphs
Adaptive thresholding for reliable topological inference in single subject fMRI analysis
Single subject fMRI has proved to be a useful tool for mapping functional areas in clinical procedures such as tumour resection. Using fMRI data, clinicians assess the risk, plan and execute such procedures based on thresholded statistical maps. However, because current thresholding methods were developed mainly in the context of cognitive neuroscience group studies, most single subject fMRI maps are thresholded manually to satisfy specific criteria related to single subject analyses. Here, we propose a new adaptive thresholding method which combines Gamma-Gaussian mixture modelling with topological thresholding to improve cluster delineation. In a series of simulations we show that by adapting to the signal and noise properties, the new method performs well in terms of the trade-off between false negative and positive cluster error rates as well as in terms of over and underestimation of the true activation border. We also show through simulations and a motor test-retest study on ten volunteer subjects that adaptive thresholding improves reliability, mainly by accounting for the global signal variance. This in turn increases the likelihood that the true activation pattern can be determined
A Multivariate Surface-Based Analysis of the Putamen in Premature Newborns: Regional Differences within the Ventral Striatum
Many children born preterm exhibit frontal executive dysfunction, behavioral problems including attentional deficit/hyperactivity disorder and attention related learning disabilities. Anomalies in regional specificity of cortico-striato-thalamo-cortical circuits may underlie deficits in these disorders. Nonspecific volumetric deficits of striatal structures have been documented in these subjects, but little is known about surface deformation in these structures. For the first time, here we found regional surface morphological differences in the preterm neonatal ventral striatum. We performed regional group comparisons of the surface anatomy of the striatum (putamen and globus pallidus) between 17 preterm and 19 term-born neonates at term-equivalent age. We reconstructed striatal surfaces from manually segmented brain magnetic resonance images and analyzed them using our in-house conformal mapping program. All surfaces were registered to a template with a new surface fluid registration method. Vertex-based statistical comparisons between the two groups were performed via four methods: univariate and multivariate tensor-based morphometry, the commonly used medial axis distance, and a combination of the last two statistics. We found statistically significant differences in regional morphology between the two groups that are consistent across statistics, but more extensive for multivariate measures. Differences were localized to the ventral aspect of the striatum. In particular, we found abnormalities in the preterm anterior/inferior putamen, which is interconnected with the medial orbital/prefrontal cortex and the midline thalamic nuclei including the medial dorsal nucleus and pulvinar. These findings support the hypothesis that the ventral striatum is vulnerable, within the cortico-stiato-thalamo-cortical neural circuitry, which may underlie the risk for long-term development of frontal executive dysfunction, attention deficit hyperactivity disorder and attention-related learning disabilities in preterm neonates. © 2013 Shi et al
Peak Detection as Multiple Testing
This paper considers the problem of detecting equal-shaped non-overlapping
unimodal peaks in the presence of Gaussian ergodic stationary noise, where the
number, location and heights of the peaks are unknown. A multiple testing
approach is proposed in which, after kernel smoothing, the presence of a peak
is tested at each observed local maximum. The procedure provides strong control
of the family wise error rate and the false discovery rate asymptotically as
both the signal-to-noise ratio (SNR) and the search space get large, where the
search space may grow exponentially as a function of SNR. Simulations assuming
a Gaussian peak shape and a Gaussian autocorrelation function show that desired
error levels are achieved for relatively low SNR and are robust to partial peak
overlap. Simulations also show that detection power is maximized when the
smoothing bandwidth is close to the bandwidth of the signal peaks, akin to the
well-known matched filter theorem in signal processing. The procedure is
illustrated in an analysis of electrical recordings of neuronal cell activity.Comment: 37 pages, 8 figure
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