Classical and Bayesian Inference in fMRI

Although there a number of methods for doing this we focus on a recent approach called Dynamic Causal Modelling (DCM).In order to assign an observed response to a particular brain structure, or cortical area, the data must conform to a known anatomical space.Before considering statistical modeling, this chapter therefore deals briefly with how a time-series of images (from single or multiple subjects) are realigned and mapped into some standard anatomical space (e.g. a stereotactic space).A central issue in this chapter is the distinction between Classical and Bayesian estimation and inference.Historically, the most popular and successful method for the analysis of fMRI is SPM.This is based on voxel-wise general linear modelling and Gaussian Random Field (GRF) theory.More recently, a number of Bayesian estimation and inference procedures have appeared in the literature.A key reason behind this is that, as our models become more realistic (and therefore complex) they need to be constrained in some way.A simple and principled way of doing this is to use priors in a Bayesian context.In this chapter we will see Bayesian methods being used in spatial normalisation (section 2.3), posterior probability mapping (section 5) and dynamic causal modelling (section 6).One should not lose sight, however, of the simplicity of the original SPM procedures (section 4) as they remain attractive both from an interpretive and computational perspective.The analysis of functional neuroimaging data involves many steps that can be broadly divided into; (i) spatial processing, (ii) estimating the parameters of a statistical model and (iii) making inferences about those parameter estimates with appropriate statistics.This data processing stream is shown in Figure 1.