As well as this standard error which is related to the number of samples we use to measure (the uncertainty in the measure), we have another uncertainty, due to repetition, or separate ``trials''.
i , i.e. the index is related to the measures whereas, on the other hand, indexes the trials. is the measure at one particular point for a particular trial and (or in prior papers), the sensitivity of the measure, is what we seek to identify.
To measure the mean of , we use the summation thus
And the errors are summarised in a messy fashion in the sets of equations below.
< > < >
is the number of repeated experiments, among the instantiations that we have.
We fit a function to the measures curve (e.g. Specificity or overlap)
and its error bars and then compute the ratio of the curve over the
mean of all inter-instantiation error bars. Error should be added
and aggregated too, in lines with some of the rules above.