Biomedical subjects

Will Penny

Publications and source records attributed to Will Penny.

6 recordsLinked to original sources

PubMed2007

Bayesian comparison of spatially regularised general linear models.

In previous work (Penny et al., [2005]: Neuroimage 24:350-362) we have developed a spatially regularised General Linear Model for the analysis of functional magnetic resonance imaging data that allows for the characterisation of regionally specific effects using Posterior Probability Maps (PPMs). In this paper we show how it also provides an approximation to the model evidence. This is important as it is the basis of Bayesian model comparison and provides a unified framework for Bayesian Analysis of Variance, Cluster of Interest analyses and the principled selection of signal and noise models. We also provide extensions that implement spatial and anatomical regularisation of noise process parameters.

Artifacts↗

PubMed2006

Variational free energy and the Laplace approximation.

This note derives the variational free energy under the Laplace approximation, with a focus on accounting for additional model complexity induced by increasing the number of model parameters. This is relevant when using the free energy as an approximation to the log-evidence in Bayesian model averaging and selection. By setting restricted maximum likelihood (ReML) in the larger context of variational learning and expectation maximisation (EM), we show how the ReML objective function can be adjusted to provide an approximation to the log-evidence for a particular model. This means ReML can be used for model selection, specifically to select or compare models with different covariance components. This is useful in the context of hierarchical models because it enables a principled selection of priors that, under simple hyperpriors, can be used for automatic model selection and relevance determination (ARD). Deriving the ReML objective function, from basic variational principles, discloses the simple relationships among Variational Bayes, EM and ReML. Furthermore, we show that EM is formally identical to a full variational treatment when the precisions are linear in the hyperparameters. Finally, we also consider, briefly, dynamic models and how these inform the regularisation of free energy ascent schemes, like EM and ReML.

Bayes Theorem↗

PubMed2004

New approaches for exploring anatomical and functional connectivity in the human brain.

Information processing in the primate brain is based on the complementary principles of modular and distributed information processing. The former emphasizes the specialization of functions within different brain areas. The latter emphasizes the massively parallel nature of brain networks and the fact that function also emerges from the flow of information between brain areas. The localization of function to specific brain areas ("functional segregation") is the commonest approach to investigating function; however, an emerging, complementary approach ("functional integration") describes function in terms of the information flow across networks of areas. Here, we highlight recent advances in neuroimaging methodology that have made it possible to investigate the anatomical architecture of networks in the living human brain with diffusion tensor imaging (DTI). We also highlight recent thinking on the ways in which functional imaging can be used to characterize information transmission across networks in the human brain (functional and effective connectivity).

Animals↗

PubMed2004

Cognitive tasks for driving a brain-computer interfacing system: a pilot study.

Different cognitive tasks were investigated for use with a brain-computer interface (BCI). The main aim was to evaluate which two of several candidate tasks lead to patterns of electroencephalographic (EEG) activity that could be differentiated most reliably and, therefore, produce the highest communication rate. An optimal signal processing method was also sought to enhance differentiation of EEG profiles across tasks. In ten normal subjects (five male), aged 29-54 years, EEG activity was recorded from four channels during cognitive tasks grouped in pairs, and performed alternately. Four imagery tasks were: spatial navigation around a familiar environment; auditory imagery of a familiar tune; and right and left motor imagery of opening and closing the hand. Signal processing methodology included autoregressive (AR) modeling and classification based on logistic regression and a nonlinear generative classifier. The highest communication rate was found using the navigation and auditory imagery tasks. In terms of classification performance and, hence, possible communication rate, these results were significantly better (p < 0.05) than those obtained with the classical pairing of motor tasks involving imaginary movements of the left and right hands. In terms of EEG data analysis, a nonlinear classification model provided more robust results than a linear model (p << 0.01), and a lower AR model order than those used in previous work was found to be effective. These findings have implications for establishing appropriate methods to operate BCI systems, particularly for disabled people who may experience difficulty with motor tasks, even motor imagery.

Adult↗

PubMed2003

Variational Bayesian inference for fMRI time series.

We describe a Bayesian estimation and inference procedure for fMRI time series based on the use of General Linear Models with Autoregressive (AR) error processes. We make use of the Variational Bayesian (VB) framework which approximates the true posterior density with a factorised density. The fidelity of this approximation is verified via Gibbs sampling. The VB approach provides a natural extension to previous Bayesian analyses which have used Empirical Bayes. VB has the advantage of taking into account the variability of hyperparameter estimates with little additional computational effort. Further, VB allows for automatic selection of the order of the AR process. Results are shown on simulated data and on data from an event-related fMRI experiment.

Algorithms↗

PubMed2003

Mixtures of general linear models for functional neuroimaging.

We set out a new general framework for making inferences from neuroimaging data, which includes a standard approach to neuroimaging analysis, statistical parametric mapping (SPM), as a special case. The model offers numerous conceptual and statistical advantages that derive from analyzing data at the "cluster level" rather than the "voxel level" and from explicit modeling of the shape and position of clusters of activation. This provides a natural and principled way to pool data from nearby voxels for parameter and variance-component estimation. The model can also be viewed as performing a spatio-temporal cluster analysis. The parameters of the model are estimated using an expectation maximization (EM) algorithm.

Acoustic Stimulation↗