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[DOC] Updates the TEDPCA section following changes in tedana v0.0.8 #551

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Mar 25, 2020
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[DOC] Updates the TEDPCA section following changes in tedana v0.0.8 #551

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[DOC] Updates the TEDPCA section following changes in tedana v0.0.8
eurunuela Mar 21, 2020
66e028f
Adds missing reference
eurunuela Mar 21, 2020
da7fa34
Adds missing line break
eurunuela Mar 21, 2020
48958c9
Reduced the math-wizardry of the MA PCA description
eurunuela Mar 23, 2020
3b4c570
Gives iid its full name
eurunuela Mar 24, 2020
1b68ebd
Update docs/approach.rst
eurunuela Mar 24, 2020
510cce5
Update docs/approach.rst
eurunuela Mar 24, 2020
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15 changes: 12 additions & 3 deletions docs/approach.rst
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Expand Up @@ -208,10 +208,18 @@ Here we can see time series for some example components (we don't really care ab
.. image:: /_static/a11_pca_component_timeseries.png

These components are subjected to component selection, the specifics of which
vary according to algorithm.
vary according to algorithm. Specifically, ``tedana`` offers two different approaches that perform this step.

In the simplest approach, ``tedana`` uses Minka’s MLE to estimate the
dimensionality of the data, which disregards low-variance components (the `mle` option in for `--tedpca`).
The default approach (the `mdl` option for `--tedpca`) is based on a Moving Average (stationary Gaussian) process
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proposed by `Li et al (2007)`_. A moving average process is the output of a linear system (which in this case is
a smoothing filter) that has an independent and identically distributed Gaussian process as the input. If we assume that the linear system is shift
invariant, the moving average process is a stationary Gaussian random process. Simply put, this process more optimally
selects the number of components for fMRI data following a subsampling scheme described in `Li et al (2007)`_. The
selection of components is performed with either of the three options provided by `--tedpca`:

* `aic`: the Akaike Information Criterion, which is the least aggressive option; i.e., returns the largest number of components.
* `kic`: the Kullback-Leibler Information Criterion, which stands in the middle in terms of aggressiveness.
* `mdl`: the Minimum Description Length, which is the most aggressive (and recommended) option.

A more complicated approach involves applying a decision tree (similar to the
decision tree described in the TEDICA section below) to identify and
Expand Down Expand Up @@ -314,3 +322,4 @@ Currently, ``tedana`` implements GSR and T1c-GSR.

.. _physics section: https://tedana.readthedocs.io/en/latest/multi_echo.html
.. _Kundu et al (2013): https://www.ncbi.nlm.nih.gov/pubmed/24038744
.. _Li et al (2007): https://onlinelibrary.wiley.com/doi/abs/10.1002/hbm.20359