.. _population_ati:

Population inference: Create a sample for further analysis
----------------------------------------------------------

Signal models have been fitted to FMRI session data:

.. code:: shell

    fmrifit -v --stimulus-block letter --window 2 1 1

    fsl4prune -v

The ATI reference field
.......................

Model based estimation encourages to analyse and report BOLD effects in
*above template image* (ATI) units. The reason is that FMRI have no
»natural« unit. If :math:`(α_j(x), x∈M)` is the intercept and
:math:`(β_j(x), x∈M)` is the estimated task related BOLD effect in an
FMRI, and if :math:`(μ_x, x∈M)` is an *ATI reference field* in standard
space :math:`M`, then

.. math::

    c_jβ_j (x) := c_j(x) ⋅ β_j(x) \quad \text { with } \quad c_j(x) =
    \frac {μ_x}{α_j(x)}

is the BOLD effect at :math:`x` in *ATI*.

As shown here_, the statistical analysis of the task related BOLD
effects benefits (by gaining power without loosing statistical validity)
when the analysis is performed with the fields :math:`c_jβ_j` and
**not** with the fields :math:`β_j`. This is in particular true for
multicentre studies.

.. _here: https://arxiv.org/abs/1809.07232v1

A reasonable choice for the ATI reference field is to chose a field with
similar curvature as the estimated statistics fields in the sample. As
this curvature is predominately influenced by the choice of the spatial
weighting scheme, a canonical choice is to smooth a template in standard
space by the same spatial weighting that has been used when fitting the
individual statistic fields.

Look for the parameter ``scale`` in one of your fits:

.. code:: shell

    fmriinfo results/WGT/AGB300/0002/AGB300-0002-WGT-2014-04-24-mni152-ants-pcm.fit

.. code:: shell

    [...]
       Hyperparameters:
            Scale type:         max
            Factor:            3.00

        Resulting in:
            Mass:            0.9973
            Scale:             2.30 mm
            FWHM:              5.42 mm
            Radius:            6.90 mm
            Diagonal:         13.80 mm
    [...]

Then create the corresponding ATI reference field:

.. code:: shell

    nii2image --name mni152 \
        /usr/share/data/fsl-mni152-templates/MNI152_T1_2mm_brain.nii.gz \
        vb-template.image

    fmriati 2.3 vb-template.image vb-ati.image -v

Create the sample for your study
................................

.. code:: shell

    fmrisample -v tutorial.sample --vb-ati-image vb-ati.image