Christopher R. Genovese

Thresholding of Statistical Maps in Functional Neuroimaging Using the False Discovery Rate

Finding objective and effective thresholds for voxelwise statistics derived from neuroimaging data has been a long-standing problem. With at least one test performed for every voxel in an image, some correction of the thresholds is needed to control the error rates, but standard procedures for multiple hypothesis testing (e.g., Bonferroni) tend to not be sensitive enough to be useful in this context. This paper introduces to the neuroscience literature statistical procedures for controlling the false discovery rate (FDR). Recent theoretical work in statistics suggests that FDR-controlling procedures will be effective for the analysis of neuroimaging data. These procedures operate simultaneously on all voxelwise test statistics to determine which tests should be considered statistically significant. The innovation of the procedures is that they control the expected proportion of the rejected hypotheses that are falsely rejected. We demonstrate this approach using both simulations and functional magnetic resonance imaging data from two simple experiments.

Maturation of widely distributed brain function subserves cognitive development.

Cognitive and brain maturational changes continue throughout late childhood and adolescence. During this time, increasing cognitive control over behavior enhances the voluntary suppression of reflexive/impulsive response tendencies. Recently, with the advent of functional MRI, it has become possible to characterize changes in brain activity during cognitive development. In order to investigate the cognitive and brain maturation subserving the ability to voluntarily suppress context-inappropriate behavior, we tested 8-30 year olds in an oculomotor response-suppression task. Behavioral results indicated that adult-like ability to inhibit prepotent responses matured gradually through childhood and adolescence. Functional MRI results indicated that brain activation in frontal, parietal, striatal, and thalamic regions increased progressively from childhood to adulthood. Prefrontal cortex was more active in adolescents than in children or adults; adults demonstrated greater activation in the lateral cerebellum than younger subjects. These results suggest that efficient top-down modulation of reflexive acts may not be fully developed until adulthood and provide evidence that maturation of function across widely distributed brain regions lays the groundwork for enhanced voluntary control of behavior during cognitive development.

Spatial updating in human parietal cortex.

Single neurons in monkey parietal cortex update visual information in conjunction with eye movements. This remapping of stimulus representations is thought to contribute to spatial constancy. We hypothesized that a similar process occurs in human parietal cortex and that we could visualize it with functional MRI. We scanned subjects during a task that involved remapping of visual signals across hemifields. We observed an initial response in the hemisphere contralateral to the visual stimulus, followed by a remapped response in the hemisphere ipsilateral to the stimulus. We ruled out the possibility that this remapped response resulted from either eye movements or visual stimuli alone. Our results demonstrate that updating of visual information occurs in human parietal cortex.

A stochastic process approach to false discovery control

This paper extends the theory of false discovery rates (FDR) pioneered by Benjamini and Hochberg [J. Roy. Statist. Soc. Ser B 57 (1995) 289-300]. We develop a framework in which the False Discovery Proportion (FDP)-the number of false rejections divided by the number of rejections-is treated as a stochastic process. After obtaining the limiting distribution of the process, we demonstrate the validity of a class of procedures for controlling the False Discovery Rate (the expected FDP). We construct a confidence envelope for the whole FDP process. From these envelopes we derive confidence thresholds, for controlling the quantiles of the distribution of the FDP as well as controlling the number of false discoveries. We also investigate methods for estimating the p-value distribution.

Cortical networks subserving pursuit and saccadic eye movements in humans: an FMRI study.

High‐field (3 Tesla) functional magnetic resonance imaging (MRI) was used to investigate the cortical circuitry subserving pursuit tracking in humans and compare it to that for saccadic eye movements. Pursuit performance, relative to visual fixation, elicited activation in three areas known to contribute to eye movements in humans and in nonhuman primates: the frontal eye field, supplementary eye field, and intraparietal sulcus. It also activated three medial regions not previously identified in human neuroimaging studies of pursuit: the precuneus and the anterior and posterior cingulate cortices. All six areas were also activated during saccades. The spatial extent of activation was similar for saccades and pursuit in all but two regions: spatial extent was greater for saccades in the superior branch of the frontal eye field and greater for pursuit in posterior cingulate cortex. This set of activations for smooth pursuit parallels the network of oculomotor areas characterized in nonhuman primates and complements recent studies showing that common cortical networks subserve oculomotor functions and spatial attention in humans. Hum. Brain Mapping 8:209–225, 1999.

Differential rotation and dynamics of the solar interior

Splitting of the suns global oscillation frequencies by large-scale flows can be used to investigate how rotation varies with radius and latitude within the solar interior. The nearly uninterrupted observations by the Global Oscillation Network Group (GONG) yield oscillation power spectra with high duty cycles and high signal-to-noise ratios. Frequency splittings derived from GONG observations confirm that the variation of rotation rate with latitude seen at the surface carries through much of the convection zone, at the base of which is an adjustment layer leading to latitudinally independent rotation at greater depths. A distinctive shear layer just below the surface is discernible at low to mid-latitudes.

False Discovery Control for Random Fields

This article extends false discovery rates to random fields, for which there are uncountably many hypothesis tests. We develop a method for finding regions in the fields domain where there is a significant signal while controlling either the proportion of area or the proportion of clusters in which false rejections occur. The method produces confidence envelopes for the proportion of false discoveries as a function of the rejection threshold. From the confidence envelopes, we derive threshold procedures to control either the mean or the specified tail probabilities of the false discovery proportion. An essential ingredient of this construnction is a new algorithm to compute a confidence superset for the set of all true-null locations. We demonstrate our method with applications to scan statistics and functional neuroimaging.

Functional Imaging Analysis Software — Computational Olio

Magnetic resonance imaging (MRI) is a modern technique for producing pictures of the internals of the human body. An MR scanner subjects its contents to carefully modulated electro-magnetic fields and records the resulting radio signal. The radio signal is the Fourier transform of the density of (for example) hydrogen atoms. Computing the inverse Fourier transform of the digitized signal reveals an image of the (hydrogen density of the) contents of the scanner. Functional MRI (fMRI) is a very recent development in which MRI is used to produce images of the human brain which show regions of activation reflecting the functioning of the brain.

A New Source Detection Algorithm Using the False-Discovery Rate

The false-discovery rate (FDR) method has recently been described by Miller et al., along with several examples of astrophysical applications. FDR is a new statistical procedure due to Benjamini & Hochberg for controlling the fraction of false positives when performing multiple hypothesis testing. The importance of this method to source detection algorithms is immediately clear. To explore the possibilities offered, we have developed a new task for performing source detection in radio telescope images, SFIND 2.0, which implements FDR. We compare SFIND 2.0 with two other source detection and measurement tasks, IMSAD and SExtractor, and comment on several issues arising from the nature of the correlation between nearby pixels and the necessary assumption of the null hypothesis. The strong suggestion is made that implementing FDR as a threshold-defining method in other existing source detection tasks is easy and worthwhile. We show that the constraint on the fraction of false detections as specified by FDR holds true even for highly correlated and realistic images. For the detection of true sources, which are complex combinations of source pixels, this constraint appears to be somewhat less strict. It is still reliable enough, however, for a priori estimates of the fraction of false source detections to be robust and realistic.The False Discovery Rate (FDR) method has recently been described by Miller et al (2001), along with several examples of astrophysical applications. FDR is a new statistical procedure due to Benjamini and Hochberg (1995) for controlling the fraction of false positives when performing multiple hypothesis testing. The importance of this method to source detection algorithms is immediately clear. To explore the possibilities offered we have developed a new task for performing source detection in radio-telescope images, Sfind 2.0, which implements FDR. We compare Sfind 2.0 with two other source detection and measurement tasks, Imsad and SExtractor, and comment on several issues arising from the nature of the correlation between nearby pixels and the necessary assumption of the null hypothesis. The strong suggestion is made that implementing FDR as a threshold defining method in other existing source-detection tasks is easy and worthwhile. We show that the constraint on the fraction of false detections as specified by FDR holds true even for highly correlated and realistic images. For the detection of true sources, which are complex combinations of source-pixels, this constraint appears to be somewhat less strict. It is still reliable enough, however, for a priori estimates of the fraction of false source detections to be robust and realistic.

A Bayesian Time-Course Model for Functional Magnetic Resonance Imaging Data

Abstract Functional magnetic resonance imaging (fMRI) is a new technique for studying the workings of the active human brain. During an fMRI experiment, a sequence of magnetic resonance images is acquired while the subject performs specific behavioral tasks. Changes in the measured signal can be used to identify and characterize the brain activity resulting from task performance. The data obtained from an fMRI experiment are a realization of a complex spatiotemporal process with many sources of variation, both biological and technological. This article describes a nonlinear Bayesian hierarchical model for fMRI data and presents inferential methods that enable investigators to directly target their scientific questions of interest, many of which are inaccessible to current methods. The article describes optimization and posterior sampling techniques to fit the model, both of which must be applied many thousands of times for a single dataset. The model is used to analyze data from a psychological experiment and to test a specific prediction of a cognitive theory.