Figure 1

ROC curves for simulated data with different wave forms. The Bayesian detector (BIC 40) with a Gaussian prior with mean 40 and standard deviation 0.1, the Fisher's g-test detector (Fisher), and the combination test detector (Lichtenberg) for the period time 40 min, were all applied to 1000 samples each from a set of simulated periodic signals and non-periodic signals. The periodic signals had period 50 min and amplitude 1, sampled at 5 min intervals over two periods (100 min). Gaussian white noise with standard deviation 1.0 was added. The set of non-periodic signals was formed by sampling a Gaussian distribution with standard deviation equal to the standard deviation of the periodic class and mean zero. Results are shown for three different waveforms, sawtooth (a), sinusoid (b) and square (c). As can be expected the detectors perform best on the sinusoidal waveform (b). The relatively larger robustness of the Bayesian detector is clearly revealed as it outperforms the other two detectors in all three cases. We also studied the effects of attenuation by multiplying each of the waveforms with an exponentially decreasing factor e^-αt (d, e, f). The attenuation coefficient α of the exponential was chosen such that the amplitude at 100 min was 70% of that at 0 min. As is seen this modification has little effect on the performance of the detectors, but naturally its performance will degrade more with faster attenuation.