Application of Bayesian inference to fMRI data analysis

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Abstract
The methods of Bayesian statistics are applied to the analysis of fMRI data. Three specific models are examined. The first is the familiar linear model with white Gaussian noise, In this section, the Jeffreys' Rule for noninformative prior distributions is stated and it is shown how the posterior distribution may be used to infer activation in individual pixels, Next, linear time-invariant (LTI) systems are introduced as an example of statistical models with nonlinear parameters, It is shown that the Bayesian approach can lead to quite complex bimodal distributions of the parameters when the specific case of a delta function response with a spatially varying delay is analyzed, Finally, a linear model with auto-regressive noise is discussed as an alternative to that with uncorrelated white Gaussian noise. The analysis isolates those pixels that have significant temporal correlation under the model, It is shown that the number of pixels that have a significantly large auto-regression parameter is dependent on the terms used to account for confounding effects.