Conclusions and Discussion

In general, the use of a fully Bayesian approach is a powerful way of considering more reasonable, and often more complex, models whilst guarding against over-fitting and giving correct inference on parameters in the model. We can consider model selection techniques to tune the modelling used and/or we can use techniques such as ARD to adaptively determine the evidence for parameters in the model. ARD is a neat trick to avoid the computational complexities of reversible jumps (27), or similar techniques. This allows us to really explore whether or not there is evidence in the data for the presence of a particular parameter, rather than assuming that there is, and consequently over-fitting and unnecessarily increasing the uncertainty in parameters of interest. The downside of this approach is that inferring on the models is not analytical and we are required to use techniques such as MCMC. These techniques are time consuming for the large datasets which are encountered in FMRI. On a 2GHz Intel PC the technique takes approximately 6 hours on a single slice of FMRI data. Whilst this is not an obstacle to exploring modelling issues as addressed in this paper, it is realistically an obstacle to using such techniques for ``everyday'' analysis of FMRI data. An alternative is to assume approximations to the posterior such as those offered by the framework of Variational Bayes (32). For example, (38) use Variational Bayes with a multivariate autoregressive temporal model. However, the most common form of Variational Bayes requires conjugate priors and is hence only tractable in the same situations as when Gibbs sampling can be used. For example, in the model used in this paper this would mean that the HRF parameters would be intractable, limiting the choice of HRF modelling to those which would be tractable (e.g. basis functions). We now discuss some of the issues in noise and signal modelling separately.