Ardo Illaste edited results_sensitivity.md  almost 10 years ago

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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  ofthe 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 originalclean signal. It is presented as a percentage of the maximal error which is obtained when no  eventregions 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