Reconstructing Mammalian Sleep Dynamics with Data Assimilation
Figure 4
Optimization of Covariance Inflater .
Although the individual EOCs are metrics of reconstruction fidelity, the ranked observability, from the full can be used to guide optimization of the covariance inflater
: Poorly observed variables across their rows - low
- should have decreased
. Variables whose measurement yields poor reconstruction columnwise- low
- should have increased
. Algorithmically, we iteratively adjust
for the variable
with the overall lowest mean row or column. In A–C are shown the
matrix after each optimization iteration for the full DB model with thalamic noise. A)
computed with default values for
, i.e.
. Note that the lowest mean row/column corresponds to the measurement of
, therefore we optimize
first. B)
after optimization of
. C)
after optimizing
. Shown are
as a function of D)
for optimization step between A and B and E)
for optimization steps between B and C. Optimal values of
are chosen from the peaks of these plots.