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The different inference approaches are all different ways of
obtaining a z-statistic for the t-contrast of interest. The
different inference approaches considered are:
- [MCMC] We sample from
to get an MCMC chain of 200,000 samples (with a burnin of 1000
samples) using the approach described in section 3.6,
we directly calculate the
from the MCMC
samples of the marginal posterior of
. We can
then use a p-to-z transform to calculate a z-statistic at each
voxel.
- [BIDET] We fit a non-central t-distribution
to an MCMC chain of 200,000 samples (with a burnin of 1000
samples) using the approach described in section 3.7.
We can then use a t-to-p-to-z transform to calculate a z-statistic
at each voxel.
- [LOWER] We use the lower bound
from the fast approximation approach described in
section 3.5 to get an approximate non-central
t-distribution. The lower bound is obtained when we assume DOF,
. We can then use a t-to-p-to-z transform to
calculate a z-statistic at each voxel.
- [UPPER] We use the upper bound
from the fast approximation approach described in
section 3.5 to get an approximate non-central
t-distribution. The upper bound is obtained when we assume DOF,
.
- [OLS] This is the
standard frequentist approach (described at the start of
section 3) of estimating the total mixed effects
variance. This ignores
. Using the total
mixed effects variance estimate, frequentist theory gives that the
normalised OLS estimate of
is t-distributed with DOF,
. We can then use a t-to-p-to-z transform to
calculate a z-statistic at each voxel.
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