Thresholding

Using [HYBRID], we obtain the marginal posterior, $p(\beta_g\vert Y)$, as a multivariate non-central t-distribution. We can then use a contrast $c=1$ to produce $p(c^T\beta_g\vert Y)$. As discussed in section 6.3 we have a number of choices as to how we infer on this posterior distribution. Here we take the option of performing a t-to-p-to-z transform and mimicking a null-hypothesis frequentist inference (i.e. controlling a FPR) by assuming that under the null hypothesis the z-statistics produced are standardised Normally distributed (see section 6.3). One advantage of doing this is that we can utilise Gaussian Random Field Theory (GRFT) (21,26). Here we use GRFT to threshold the z-statistic maps and generate activation clusters determined by $z>2.3$ with a significance threshold of $p=0.01$.