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- Karl J. Friston, L M Harrison, W . D . Penny
- NeuroImage
- 2003

In this paper we present an approach to the identification of nonlinear input-state-output systems. By using a bilinear approximation to the dynamics of interactions among states, the parameters of the implicit causal model reduce to three sets. These comprise (1) parameters that mediate the influence of extrinsic inputs on the states, (2) parameters that… (More)

- W . D . Penny, Klaas Enno Stephan, Andrea Mechelli, Karl J. Friston
- NeuroImage
- 2004

This article describes the use of Bayes factors for comparing dynamic causal models (DCMs). DCMs are used to make inferences about effective connectivity from functional magnetic resonance imaging (fMRI) data. These inferences, however, are contingent upon assumptions about model structure, that is, the connectivity pattern between the regions included in… (More)

- Karl J. Friston, W . D . Penny, Chris Phillips, Stephan J Kiebel, Geoff Hinton, John Ashburner
- NeuroImage
- 2002

This paper reviews hierarchical observation models, used in functional neuroimaging, in a Bayesian light. It emphasizes the common ground shared by classical and Bayesian methods to show that conventional analyses of neuroimaging data can be usefully extended within an empirical Bayesian framework. In particular we formulate the procedures used in… (More)

- W . D . Penny, Klaas Enno Stephan, Andrea Mechelli, Karl J. Friston
- NeuroImage
- 2004

The brain appears to adhere to two fundamental principles of functional organisation, functional integration and functional specialisation, where the integration within and among specialised areas is mediated by effective connectivity. In this paper, we review two different approaches to modelling effective connectivity from fMRI data, structural equation… (More)

- Karl J. Friston, W . D . Penny
- 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, given the data. Posterior probability maps (PPMs) represent… (More)

- L M Harrison, W . D . Penny, Karl J. Friston
- NeuroImage
- 2003

We propose the use of multivariate autoregressive (MAR) models of functional magnetic resonance imaging time series to make inferences about functional integration within the human brain. The method is demonstrated with synthetic and real data showing how such models are able to characterize interregional dependence. We extend linear MAR models to… (More)

- W . D . Penny, Emrah Duzel, K.J. Miller, J Ojemann
- Journal of Neuroscience Methods
- 2008

Nested oscillation occurs when the amplitude of a faster rhythm is coupled to the phase of a slower rhythm. It has been proposed to underlie the discrete nature of perception and the capacity of working memory and is a phenomenon observable in human brain imaging data. This paper compares three published methods for detecting nested oscillation and a fourth… (More)

- M.J. Rosa, Karl J. Friston, W . D . Penny
- Journal of Neuroscience Methods
- 2012

Dynamic causal modelling (DCM) was originally proposed as a hypothesis driven procedure in which a small number of neurobiologically motivated models are compared. Model comparison in this context usually proceeds by individually fitting each model to data and then approximating the corresponding model evidence with a free energy bound. However, a recent… (More)

- W . D . Penny, Vladimir Litvak, Lluís Fuentemilla, Emrah Duzel, Karl J. Friston
- Journal of Neuroscience Methods
- 2009

This paper presents an extension of the Dynamic Causal Modelling (DCM) framework to the analysis of phase-coupled data. A weakly coupled oscillator approach is used to describe dynamic phase changes in a network of oscillators. The use of Bayesian model comparison allows one to infer the mechanisms underlying synchronization processes in the brain. For… (More)

- W . D . Penny
- 2006

The mainstay of many scientific experiments is the factorial design. These comprise a number of experimental factors which are each expressed over a number of levels. Data are collected for each factor/level combination and then analysed using analysis of variance (ANOVA). The ANOVA uses F-tests to examine a pre-specified set of standard effects, e.g. ‘main… (More)