...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 $ \boldsymbol {q}$ 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 $ (r,c)$, $h$ is computed under the assumption that $r$ and $c$ were targets. However, only if $ (r,c)$ is the true target character $ (\hat r, \hat c)$, the variables controlling the weight, % latex2html id marker 7336
$ H^{\Romannum {1}}$ and % latex2html id marker 7338
$ H^{\Romannum {2}}$, match the ones determining the average amplitude; in all other cases the flash score is weighted with a ``wrong'' $h$.
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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 $ \mathrm{w}(h)=1
\; \forall h$. 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 $ S_{\hat r, \hat c}$ is very low for values of $ \mathrm{w}(h)$ reasonably close to 1 (we will show later that this is indeed the case for our experiment).
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