In this paper we present an approach to making inferences about generic activations in groups of subjects using fMRI. In particular we suggest that activations common to all subjects reflect aspects of functional anatomy that may be ‘‘typical’ ’ of the population from which that group was sampled. These commonalities can be identified by a conjunction analysis of the activation effects in which the contrasts, testing for an activation, are specified separately for each subject. A conjunction is the joint refutation of multiple null hypotheses, in this instance, of no activation in any subject. The motivation behind this use of conjunctions is that fixed-effect analyses are generally more ‘‘sensitive’ ’ than equivalent random-effect analyses. This is because fixed-effect analyses can harness the large degrees of freedom and small scan-to-scan variability (relative to the variability in responses from subject to subject) when assessing the significance of an estimated response. The price one pays for the apparent sensitivity of fixed-effect analyses is that the ensuing inferences pertain to, and only to, the subjects studied. However, a conjunction analysis, using a fixedeffect model, allows one to infer: (i) that every subject studied activated and (ii) that at least a certain proportion of the population would have shown this effect. The second inference depends upon a meta-analytic formulation in terms of a confidence region for this proportion. This approach retains the sensitivity of fixed-effect analyses when the inference that only a substantial proportion of the population activates is sufficient.

introduced empirical Bayes as a potentially useful way to estimate and make inferences about effects in hierarchical models. In this paper we present a series of models that exemplify the diversity of problems that can be addressed within this framework. In hierarchical linear observation models, both classical and empirical Bayesian approaches can be framed in terms of covariance component estimation (e.g., variance partitioning). To illustrate the use of the expectation– maximization (EM) algorithm in covariance component estimation we focus first on two important problems in fMRI: nonsphericity induced by (i) serial or temporal correlations among errors and (ii) variance components caused by the hierarchical nature of multisubject studies. In hierarchical observation models,

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 single-event 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.

This paper concerns temporal filtering in fMRI timeseries analysis. Whitening serially correlated data is the most efficient approach to parameter estimation. However, if there is a discrepancy between the assumed and the actual correlations, whitening can render the analysis exquisitely sensitive to bias when estimating the standard error of the ensuing parameter estimates. This bias, although not expressed in terms of the estimated responses, has profound effects on any statistic used for inference. The special constraints of fMRI analysis ensure that there will always be a misspecification of the assumed serial correlations. One resolution of this problem is to filter the data to minimize bias, while maintaining a reasonable degree of efficiency. In this paper we present expressions for efficiency (of parameter estimation) and bias (in estimating standard error) in terms of assumed and actual correlation structures in the context of the general linear model. We show that: (i) Whitening strategies can result in profound bias and are therefore probably precluded in parametric fMRI data analyses. (ii) Band-pass filtering, and implicitly smoothing, has an important role in protecting against inferential

The assessment of significant activations in functional imaging using voxel-based methods often relies on results derived from the theory of Gaussian random fields. These results solve the multiple comparison problem and assume that the spatial correlation or smoothness of the data is known or can be estimated. End results (i.e., P values associated with local maxima, clusters, or sets of clusters) critically depend on this assessment, which should be as exact and as reliable as possible. In some earlier implementations of statistical parametric mapping (SPM) (SPM94, SPM95) the smoothness was assessed on Gaussianized t-fields (Gt-f) that are not generally free of physiological signal. This technique has two limitations. First, the estimation is not stable (the variance of the estimator being far from negligible) and, second, physiological signal in the Gt-f will bias the estimation. In this paper, we describe an estimation method that overcomes these drawbacks. The new approach involves estimating the smoothness of standardized residual fields which approximates the smoothness of the component fields of the associated t-field. Knowing the smoothness of these component fields is important because it allows one to compute corrected P values for statistical fields other than the t-field or the Gt-f (e.g., the F-map) and eschews bias due to deviation from the null hypothesis. We validate the method on simulated data and demonstrate it using data from a functional MRI study. � 1999 Academic Press

We apply nine analytic methods employed currently in imaging neuroscience to simulated and actual BOLD fMRI signals and compare their performances under each signal type. Starting with baseline time series generated by a resting subject during a null hypothesis study, we compare method performance with embedded focal activity in these series of three different types whose magnitudes and time courses are simple, convolved with spatially varying hemodynamic responses, and highly spatially interactive. We then apply these same nine methods to BOLD fMRI time series from contralateral primary motor cortex and ipsilateral cerebellum collected during a sequential finger opposition study. Paired comparisons of results across methods include a voxel-specific concordance correlation

INTRODUCTION In recent ERP-studies, brain responses reflecting the processing of musical chord-sequences were similar, although not identical, to brain activity elicited during the perception of language, in both musicians (Patel et al., 1998; Koelsch et al., in press) and nonmusicians (Koelsch et al., 2000a, 2001, 2002). While relatively early (around 180--350 ms) electrical brain responses to unexpected items in a structured sequence were often lateralized to the left when processing language (Friederici et al., 1993; Hahne and Friederici, 1999), they were often lateralized to the right when processing music (Patel et al., 1998; Koelsch et al., 2000a). The early brain responses (maximal around 200--350 ms) elicited by violations of musical regualrities were taken to reflect the processing of music-syntactic information (Patel et al., 1998; Koelsch et al., 2000a). Later brain responses (maximal around 500--550 ms) were hypothesized to reflect the processing of meaning information in

Is our knowledge about the appearance of objects more closely related to verbal thought or to perception? In a behavioural study using a property verification task, Kosslyn (1976) reported that there are both amodal and perceptual representations of concepts, but that amodal representations may be more easily accessed. However, Solomon (1997) argued that due to the nature of Kosslyn’s stimuli, subjects may be able to bypass semantics entirely and perform this task using differences in the strength of association between words in true trials (e.g., cat–whiskers) and those in false trials (e.g., mouse–stinger). Solomon found no evidence for amodal representations when the task materials were altered to include associated false trials (e.g., cat–litter), which require semantic processing, as opposed to associative strategies. In the current study, we used fMRI to examine the response of regions of visual association cortex while subjects performed a property verification task with either associated or unassociated false trials. We found reliable activity across subjects within the left fusiform gyrus when true trials were intermixed with associated false trials but not when true trials were intermixed with unassociated false trials. Our data support the idea that conceptual knowledge is organised visually and that it is grounded in the perceptual system. One of the leading theories of the organisation of

This paper reviews and compares individual voxel-wise thresholding methods for identifying active voxels in single-subject fMRI datasets. Different error rates are described which may be used to calibrate activation thresholds. We discuss methods which control each of the error rates at a prespecified level a, including simple procedures which ignore spatial correlation among the test statistics as well as more elaborate ones which incorporate this correlation information. The operating characteristics of the methods are shown through a simulation study, indicating that the error rate used has an important impact on the sensitivity of the thresholding method, but that accounting for correlation has little impact. Therefore, the simple procedures described work well for thresholding most single-subject fMRI experiments and are recommended. The methods are illustrated with a real bilateral finger tapping experiment

this article, we propose a procedure called Enhanced FDR (EFDR), which is based on controlling the false discovery rate (FDR) and a concept known as generalized degrees of freedom (GDF). EFDR differs from the standard FDR procedure through its reducing of the number of hypotheses tested. This is done in two ways: first, the model is represented more parsimoniously in the wavelet domain, and second, an optimal selection of hypotheses is made using a criterion based on generalized degrees of freedom. Not only does the EFDR procedure tell us whether a spatial signal is present or not, it has an added bonus that, if a signal is deemed present, it can indicate its location and magnitude. We examine EFDR's operating characteristics, and in simulations we show that it outperforms the standard FDR and conventional testing procedures. Finally, the EFDR procedure is applied to an air-temperature data set generated from the Climate System Model (CSM) of the National Center for Atmospheric Research (NCAR), where air temperatures in the 1980s are compared to those in the 1990s. We conclude that temperature change has occurred between the two decades, mostly warming in the central part of the USA and in coastal regions of South America at about 20 S. Key words: Denoising, false discovery rate, generalized degrees of freedom, pixel, power, signal detection, wavelets