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## Sensitivity analysis
### Pixel trace
As the amount of noise in the signal increases the performance of the event detection algorithm should decrease (Fig X A). The sensitivity of the method
to noise was explored by estimating
both the
probabilty probability of detecting an event
in a noisy signal and the accuracy of the fit. The original signal to be fitted was generated from the fitting function for
various five different amplitudes. To this signal different levels of normally distributed noise was
added. added (noise level is the standard deviation of the noise distribution).
Figure x
B shows the probability of detecting the event in the
signal. As the amplitude signal as a function of
the event increases so does the noise
level at which the the probability of detecting level. Increasing the event
goes below a given treshold (0.95 on amplitude shifts the
figure). event detection probability curve towards higher noise levels and vice-versa. It is more informative to look at the relationship between detection probability and the signal to noise ratio of the event. This is calculated as:
\[
SNR = \frac{\frac{1}{b-a}{\int_a^b f(t)^2\,dt}}{\sigma_n^2}
\]
where *a* and *b* are times, before and after the peak respectively, when the fluorescence is at half of its peak value (i.e., *b-a* is FDHM), *f(t)* is the event signal and \(\sigma_n\) the standard deviation of the
noise. noise (i.e., noise level).
The resulting plot is depicted on figure
x, x C, and it can be seen that detection probability is only dependent on the *SNR*. For visual comparison, the appearance of 4 events with different *SNR* and detection probabilities are shown on Figure x.
The On Figure X D the accuracy of the fit
is calculated as the average square difference between the fit and compared to the original
clean signal. It is presented as a percentage of the maximal error which is obtained when no event
regions are detected and the entire signal is
fitted with just the baseline function. Since the baseline function is a fourth order polynomial it can fit estimated for various amplitudes and noise levels as the
signal to some degree (e.g., \(R^2\) value. Predicatably the \(R^2\) value
of decreases as the
fit is 0.41 for amount of noise increases. Again, the
example in Figure x). Therefore Curves \(R^2\) curves calculated for different amplitudes overlap when plotted as a function of *SNR*.
Combining plots XC and XE the relationship between the probability of finding an event and the accuracy of the fit can be obtained.
###Release event detection