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82
submitted). Mixedeffects modeling with crossed random effects for subjects and items
, 2007
"... and items ..."
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 79 (5 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
General MultiLevel Linear Modelling for Group Analysis in FMRI
 NeuroImage
, 2003
"... This paper discusses general modelling of multisubject and/or multisession FMRI data. In particular, we show that a twolevel mixedeffects model (where parameters of interest at the group level are estimated from parameter and variance estimates from the singlesession level) can be made equivale ..."
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Cited by 62 (8 self)
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This paper discusses general modelling of multisubject and/or multisession FMRI data. In particular, we show that a twolevel mixedeffects model (where parameters of interest at the group level are estimated from parameter and variance estimates from the singlesession level) can be made equivalent to a single complete mixedeffects model (where parameters of interest at the group level are estimated directly from all of the original singlesessions' timeseries data) if the (co)variance at the second level is set equal to the sum of the (co)variances in the singlelevel form, using the BLUE with known covariances. This result has significant implications for group studies in FMRI, since it shows that the group analysis only requires values of the parameter estimates and their (co)variance from the first level, generalising the well established 'summary statistics' approach in FMRI. The simple and generalised framework allows for different prewhitening and different firstlevel regressors to be used for each subject. The framework incorporates multiple levels and cases such as repeated measures, paired or unpaired ttests and F tests at the group level; explicit examples of such models are given in the paper. Using numerical simulations based on typical first level covariance structures from real FMRI data we demonstrate that by taking into account lowerlevel covariances and heterogeneity a substantial increase in higherlevel Zscore is possible. 1
Classical and Bayesian inference in neuroimaging: applications
 NeuroImage
"... 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, bo ..."
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Cited by 57 (12 self)
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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,
A neural mass model for MEG/EEG: coupling and neuronal dynamics
 NeuroImage
, 2003
"... Although MEG/EEG signals are highly variable, systematic changes in distinct frequency bands are commonly encountered. These frequencyspecific changes represent robust neural correlates of cognitive or perceptual processes (for example, alpha rhythms emerge on closing the eyes). However, their func ..."
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Cited by 54 (20 self)
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Although MEG/EEG signals are highly variable, systematic changes in distinct frequency bands are commonly encountered. These frequencyspecific changes represent robust neural correlates of cognitive or perceptual processes (for example, alpha rhythms emerge on closing the eyes). However, their functional significance remains a matter of debate. Some of the mechanisms that generate these signals are known at the cellular level and rest on a balance of excitatory and inhibitory interactions within and between populations of neurons. The kinetics of the ensuing population dynamics determine the frequency of oscillations. In this work we extended the classical nonlinear lumpedparameter model of alpha rhythms, initially developed by Lopes da Silva and colleagues [Kybernetik 15 (1974) 27], to generate more complex dynamics. We show that the whole spectrum of MEG/EEG signals can be reproduced within the oscillatory regime of this model by simply changing the population kinetics. We used the model to examine the influence of coupling strength and propagation delay on the rhythms generated by coupled cortical areas. The main findings were that (1) coupling induces phaselocked activity, with a phase shift of 0 or π when the coupling is bidirectional, and (2) both coupling and propagation delay are critical determinants of the MEG/EEG spectrum. In forthcoming articles, we will use this model to (1) estimate how neuronal interactions are expressed in MEG/EEG oscillations and establish the construct validity of various indices of nonlinear coupling, and (2) generate eventrelated transients to derive physiologically informed basis functions for statistical modelling of average evoked responses.
Bayesian Estimation of Dynamical Systems: An Application to fMRI
 NeuroImage
, 2002
"... This paper presents a method for estimating the conditional or posterior distribution of the parameters of deterministic dynamical systems. The procedure conforms to an EM implementation of a Gauss–Newton search for the maximum of the conditional or posterior density. The inclusion of priors in the ..."
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Cited by 51 (24 self)
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This paper presents a method for estimating the conditional or posterior distribution of the parameters of deterministic dynamical systems. The procedure conforms to an EM implementation of a Gauss–Newton search for the maximum of the conditional or posterior density. The inclusion of priors in the estimation procedure ensures robust and rapid convergence and the resulting conditional densities enable Bayesian inference about the model parameters. The method is demonstrated using an input–state–output model of the hemodynamic coupling between experimentally designed causes or factors in fMRI studies and the ensuing BOLD response. This example represents a generalization of current fMRI analysis models that accommodates nonlinearities and in which the parameters have an explicit physical interpretation. Second, the approach extends classical inference, based on the likelihood of the data given a null hypothesis about the parameters, to more plausible inferences about the parameters of the model given the data. This inference provides for confidence intervals based on the
Posterior probability maps and SPMs
 NeuroImage
, 2003
"... This technical note describes the construction of posterior probability maps that enable conditional or Bayesian inferences about regionally specific effects in neuroimaging. Posterior probability maps are images of the probability or confidence that an activation exceeds some specified threshold, g ..."
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Cited by 40 (8 self)
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This technical note describes the construction of posterior probability maps that enable conditional or Bayesian inferences about regionally specific effects in neuroimaging. Posterior probability maps are images of the probability or confidence that an activation exceeds some specified threshold, given the data. Posterior probability maps (PPMs) represent a complementary alternative to statistical parametric maps (SPMs) that are used to make classical inferences. However, a key problem in Bayesian inference is the specification of appropriate priors. This problem can be finessed using empirical Bayes in which prior variances are estimated from the data, under some simple assumptions about their form. Empirical Bayes requires a hierarchical observation model, in which higher levels can be regarded as providing prior constraints on lower levels. In neuroimaging, observations of the same effect over voxels provide a natural, twolevel hierarchy that enables an empirical Bayesian approach. In this note we present a brief motivation and the operational details of a simple empirical Bayesian method for computing posterior probability maps. We then compare Bayesian and classical inference through the equivalent PPMs and SPMs testing for the same effect in the same data.
Dynamic causal modelling of evoked responses
 in EEG and MEG. NeuroImage
"... EEG/MEG with lead field parameterization ..."
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 34 (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.