- ...
^{1}
- In principle, the Monte Carlo technique we have used to
validate our model would itself need to be
validated. We have not done
a direct validation of this because of the technical difficulties
and need for large datasets associated with such a validation.
However, one should not infer from this that nothing has been proved
in this section. The chances of two radically distinct and
independent approaches to modelling a system as complex as Donchin's
speller giving almost identical results and, yet, being both
incorrect, are very low. Also, as we will see in
section 7.1, optimising
based on the
predictions of our model and then testing the system on independent
data gives accuracy improvements almost identical to those predicted
by the model. So, in reality, Monte Carlo simulations, our
theoretical model and the testing of our scoring algorithm on unseen
data corroborate one another.
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- ...
^{2}
- Note that the variables resulting from the replacement of a
star with a row or column index are different variables with the
same distribution. Also, note that during online use of a
classifier the true target is unknown. In our approach, when scoring
a generic character , is computed under the assumption
that and were targets. However, only if is the true
target character
, the variables controlling the
weight,
and
, match the ones determining
the average amplitude; in all other cases the flash score is
weighted with a ``wrong'' .
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- ...
^{3}
- This simplified model would be mistaken only if there is a non-target
whose score is higher than the target's, which in turn is higher than
all the ``half-targets''. However, this is impossible if
. So, considering only the half-targets introduces no
approximation in the calculations of the speller's accuracy when applied to the traditional non-weighted scoring scheme
in (1). Also, the likelihood of non-targets having
scores larger than
is very low for values of
reasonably close to 1 (we will show later that this is
indeed the case for our experiment).
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