We start in section 2 by considering the traditional two-level model. In section 3, using the reference analysis fully Bayesian framework, we show how inference on the two-level model can be split into separate inference on the two levels with the summary statistics of a multivariate non-central t-distribution being passed between the two-levels of inference. We then propose two approaches to inferring at the top level. In section 4 we discuss how we can extend the split model inference approach to higher level models than the two-level model. In section 5 we also discuss how we can deal with multiple group variances under certain conditions. In section 6 we validate the crucial assumption of the marginal distribution of the GLM regressions parameters being a multivariate non-central t-distribution at levels higher than the first using artificial data. Finally, in section 7 we go on to show results on FMRI data.