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- K J Friston, L Harrison, W 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, K E Stephan, A Mechelli, K 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)

- K J Friston, W Penny, C Phillips, S Kiebel, G Hinton, J 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, K E Stephan, A Mechelli, K 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)

- L Harrison, W D Penny, K 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)

- K J Friston, W 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)

- W.D. Penny, E. Duzel, K.J. Miller, J.G. 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)

- W.D. Penny, V. Litvak, L. Fuentemilla, E. Duzel, K. 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, J Kilner, F Blankenburg
- NeuroImage
- 2007

We describe a Bayesian learning algorithm for Robust General Linear Models (RGLMs). The noise is modeled as a Mixture of Gaussians rather than the usual single Gaussian. This allows different data points to be associated with different noise levels and effectively provides a robust estimation of regression coefficients. A variational inference framework is… (More)

Neural networks are parallel, distributed, adaptive information-processing systems that develop their functionality in response to exposure to information. This paper is a tutorial for researchers intending to use neural nets for medical decision-making applications. It includes detailed discussion of the issues particularly relevant to medical data as well… (More)