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235
A unified statistical approach for determining significant signals in images of cerebral activation
, 1996
"... Abstract: We present a unified statistical theory for assessing the significance of apparent signal observed in noisy difference images. The results are usable in a wide range of applications, including astrophysics, but are discussed with particular reference to images which represent changes in ce ..."
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Cited by 377 (38 self)
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Abstract: We present a unified statistical theory for assessing the significance of apparent signal observed in noisy difference images. The results are usable in a wide range of applications, including astrophysics, but are discussed with particular reference to images which represent changes in cerebral blood flow elicited by a specific cognitive or sensorimotor task. Our main result is an estimate of the pvalue for local maxima of Gaussian, t, χ 2 and F fields over search regions of any shape or size in any number of dimensions. This unifies the pvalues for large search areas in 2D (Friston et al. 1991), large search regions in 3D (Worsley et al. 1992), and the usual uncorrected pvalue at a single pixel or voxel.
Nonparametric Permutation Tests for Functional Neuroimaging: A Primer with Examples. Human Brain Mapping
, 2001
"... The statistical analyses of functional mapping experiments usually proceeds at the voxel level, involving the formation and assessment of a statistic image: at each voxel a statistic indicating evidence of the experimental effect of interest, at that voxel, is computed, giving an image of statistics ..."
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Cited by 376 (10 self)
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The statistical analyses of functional mapping experiments usually proceeds at the voxel level, involving the formation and assessment of a statistic image: at each voxel a statistic indicating evidence of the experimental effect of interest, at that voxel, is computed, giving an image of statistics, a statistic
Advances in functional and structural mr image analysis and implementation as fsl
 NeuroImage
, 2004
"... The techniques available for the interrogation and analysis of neuroimaging data have a large influence in determining the flexibility, sensitivity and scope of neuroimaging experiments. The development of such methodologies has allowed investigators to address scientific questions which could not p ..."
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Cited by 233 (6 self)
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The techniques available for the interrogation and analysis of neuroimaging data have a large influence in determining the flexibility, sensitivity and scope of neuroimaging experiments. The development of such methodologies has allowed investigators to address scientific questions which could not previously be answered and, as such, has become an important research area in its own right. In this paper, we present a review of the research carried out by the Analysis Group at the Oxford Centre for Functional MRI of the Brain (FMRIB). This research has focussed on the development of new methodologies for the analysis of both structural and functional magnetic resonance imaging data. The majority of the research laid out in this paper has been implemented as freely available software tools within FMRIB’s Software Library (FSL). 1
Temporal autocorrelation in univariate linear modelling of fMRI data
 pP Y C W P k nk N p Var(Yk ) (Yk ) 0 1 C CR 1 Var(Y ) P k nk N Var(Y k ) 0 1 C MI H(X;Y ) H(X) H(Y ) 1 0 C NMI H(X;Y ) H(X)+H(Y
, 2000
"... In functional magnetic resonance imaging statistical analysis there are problems with accounting for temporal autocorrelations when assessing change within voxels. Techniques to date have utilized temporal filtering strategies to either shape these autocorrelations or remove them. Shaping, or “color ..."
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Cited by 197 (10 self)
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In functional magnetic resonance imaging statistical analysis there are problems with accounting for temporal autocorrelations when assessing change within voxels. Techniques to date have utilized temporal filtering strategies to either shape these autocorrelations or remove them. Shaping, or “coloring, ” attempts to negate the effects of not accurately knowing the intrinsic autocorrelations by imposing known autocorrelation via temporal filtering. Removing the autocorrelation, or “prewhitening, ” gives the best linear unbiased estimator, assuming that the autocorrelation is accurately known. For singleevent designs, the efficiency of the estimator is considerably higher for prewhitening compared with coloring. However, it has been suggested that sufficiently accurate estimates of the autocorrelation are currently not available to give prewhitening acceptable bias. To overcome this, we consider different ways to estimate the autocorrelation for use in prewhitening. After highpass filtering is performed, a Tukey taper (set to smooth the spectral density more than would normally be used in spectral density estimation) performs best. Importantly, estimation is further improved by using nonlinear spatial filtering to smooth the estimated autocorrelation, but only within tissue type. Using this approach when prewhitening reduced bias to close to zero at probability levels as low as 1 � 10 �5. © 2001 Academic Press Key Words: FMRI analysis; GLM; temporal filtering; temporal autocorrelation; spatial filtering; singleevent; autoregressive model; spectral density estimation; multitapering.
Controlling the familywise error rate in functional neuroimaging: a comparative review
 Statistical Methods in Medical Research
, 2003
"... Functional neuroimaging data embodies a massive multiple testing problem, where 100 000 correlated test statistics must be assessed. The familywise error rate, the chance of any false positives is the standard measure of Type I errors in multiple testing. In this paper we review and evaluate three a ..."
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Cited by 167 (7 self)
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Functional neuroimaging data embodies a massive multiple testing problem, where 100 000 correlated test statistics must be assessed. The familywise error rate, the chance of any false positives is the standard measure of Type I errors in multiple testing. In this paper we review and evaluate three approaches to thresholding images of test statistics: Bonferroni, random �eld and the permutation test. Owing to recent developments, improved Bonferroni procedures, such as Hochberg’s methods, are now applicable to dependent data. Continuous random �eld methods use the smoothness of the image to adapt to the severity of the multiple testing problem. Also, increased computing power has made both permutation and bootstrap methods applicable to functional neuroimaging. We evaluate these approaches on t images using simulations and a collection of real datasets. We �nd that Bonferronirelated tests offer little improvement over Bonferroni, while the permutation method offers substantial improvement over the random �eld method for low smoothness and low degrees of freedom. We also show the limitations of trying to �nd an equivalent number of independent tests for an image of correlated test statistics. 1
Analysis of fMRI timeseries revisited – again
 NeuroImage
, 1995
"... Friston et al. (1995) presented a method for detecting activations in fMRI timeseries based on the general linear model and a heuristic analysis of the effective degrees of freedom. In this communication we present corrected results that replace those of the previous paper and solve the same proble ..."
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Cited by 163 (9 self)
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Friston et al. (1995) presented a method for detecting activations in fMRI timeseries based on the general linear model and a heuristic analysis of the effective degrees of freedom. In this communication we present corrected results that replace those of the previous paper and solve the same problem without recourse to heuristic arguments. Specifically we introduce a proper and unbiased estimator for the error terms and provide a more generally correct expression for the effective degrees of freedom. The previous estimates of error variance were biased, and in some instances could have led to a 1020 % overestimate of Z values. Although the previous results are almost correct for the random regressors chosen for validation, the present theoretical results are exact for any covariate or waveform. We comment on some aspects of experimental design and data analysis, in the light of the theoretical framework discussed here. Running title:
Local maxima and the expected Euler characteristic of excursion sets of χ², F and t fields
, 1994
"... The maximum of a Gaussian random field was used by Worsley et al. (... ..."
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Cited by 141 (23 self)
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The maximum of a Gaussian random field was used by Worsley et al. (...
Separating processes within a trial in eventrelated functional MRI. I. The method. NeuroImage 13
, 2001
"... Many cognitive processes occur on time scales that can significantly affect the shape of the blood oxygenation leveldependent (BOLD) response in eventrelated functional MRI. This shape can be estimated from event related designs, even if these processes occur in a fixed temporal sequence (J. M. Oll ..."
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Cited by 104 (3 self)
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Many cognitive processes occur on time scales that can significantly affect the shape of the blood oxygenation leveldependent (BOLD) response in eventrelated functional MRI. This shape can be estimated from event related designs, even if these processes occur in a fixed temporal sequence (J. M. Ollinger, G. L. Shulman, and M. Corbetta. 2001. NeuroImage 13: 210–217). Several important considerations come into play when interpreting these time courses. First, in single subjects, correlations among neighboring time points give the noise a smooth appearance that can be confused with changes in the BOLD response. Second, the variance and degree of correlation among estimated time courses are strongly influenced by the timing of the experimental design. Simulations show that optimal results are obtained if the intertrial intervals are as short as possible, if they follow an exponential distribution with at least three distinct values, and if 40 % of the trials are partial trials. These results are not particularly sensitive to the fraction of partial trials, so accurate estimation of time courses can be obtained with lower percentages of partial trials (20–25%). Third, statistical maps can be formed from F statistics computed with the extra sum of square principle or by t statistics computed from the crosscorrelation of the time courses with a model for the hemodynamic response. The latter method relies on an accurate model for the hemodynamic response. The most robust model among those tested was a single gamma function. Finally, the power spectrum of the measured BOLD signal in rapid eventrelated paradigms is similar to that of the noise. Nevertheless, highpass filtering is desirable if the appropriate model
Multilevel linear modelling for FMRI group analysis using Bayesian inference
 Neuroimage
, 2004
"... Functional magnetic resonance imaging studies often involve the acquisition of data from multiple sessions and/or multiple subjects. A hierarchical approach can be taken to modelling such data with a general linear model (GLM) at each level of the hierarchy introducing different random effects varia ..."
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Cited by 81 (6 self)
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Functional magnetic resonance imaging studies often involve the acquisition of data from multiple sessions and/or multiple subjects. A hierarchical approach can be taken to modelling such data with a general linear model (GLM) at each level of the hierarchy introducing different random effects variance components. Inferring on these models is nontrivial with frequentist solutions being unavailable. A solution is to use a Bayesian framework. One important ingredient in this is the choice of prior on the variance components and toplevel regression parameters. Due to the typically small numbers of sessions or subjects in neuroimaging, the choice of prior is critical. To alleviate this problem, we introduce to neuroimage modelling the approach of reference priors, which drives the choice of prior such that it is noninformative in an informationtheoretic sense. We propose two inference techniques at the top level for multilevel hierarchies (a fast approach and a slower more accurate approach). We also demonstrate that we can infer on the top level of multilevel hierarchies by inferring on the levels of the hierarchy separately and passing summary statistics of a noncentral multivariate t distribution between them.
Empirical analyses of BOLD fMRI statistics: II. Spatially smoothed data collected under nullhypothesis and experimental conditions
 NeuroImage
, 1997
"... 000), we describe an implementation of a general linear model for autocorrelated observations in which the voxelwise falsepositive rates in fMRI ‘‘noise’’ datasets were stabilized and brought close to theoretical values. Here, implementations of the model are tested for use with statistical param ..."
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Cited by 68 (6 self)
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000), we describe an implementation of a general linear model for autocorrelated observations in which the voxelwise falsepositive rates in fMRI ‘‘noise’’ datasets were stabilized and brought close to theoretical values. Here, implementations of the model are tested for use with statistical parametric mapping analysis of spatially smoothed fMRI data. Analyses using varying models of intrinsic temporal autocorrelation andeither including or excluding a global signal covariatewere conducted uponhuman subject data collected under null hypothesis as well as under experimental conditions. We found that smoothing with an empirically derived impulse response function (IRF), combinedwith amodel of the intrinsic temporal autocorrelation in spatially smoothed fMRI data, resulted in a mapwise falsepositive rate which did not exceed a 5% level when a nominal a 5 0.05 tabular threshold was applied.Useofothermodelsof intrinsic temporalautocorrelation resulted in mapwise falsepositive rates that significantly exceeded this level. fMRI data collected while subjects performed a behavioral task were used to examine (a) taskdependent global signal changes and (b) the dependence of sensitivity on the temporal smoothing kernel and inclusion/exclusion of a global signal covariate. The global signal changes within an fMRI dataset were shown to be influenced by the performance of a behavioral task. However, the inclusion of this measure as a covariate did not have an adverse affect upon our measure of sensitivity. Finally, use of an empirically derived estimate of the IRF of the system was shown to result in greatermapwise sensitivity for signal changes than the use of a broader (in time)