I have data consisting of radial velocities and times (covering about 10 000 days). The radial velocity changes with a period. I tried to find out the period using Stellingwerf's method (it was successful), and then I applied the bootstrap method to determine the uncertainty. I obtained a histogram that is very different from the Gaussian curve. What could be the cause?
I hope that someone more knowledgeable than me will answer this question, but this is what I understand it is happening.
The bootstrap method gives an estimate of the probability distribution of the period, given the data. If the probability distribution were a Gaussian centered on the true period, you would probably see a Gaussian.
But when estimating the period of a radial velocity signal, this is often not the case. By looking at a peridogram, you see that there are many peaks, corresponding to the true period, to its harmonics and to other artifacts. In some cases it may even happen that a spurious peak is higher than the true period peak.
This is exactly what happens with the bootstrap method. You sample your data differently and as a result you may get one of the spurious peaks as the higher one and incorrectly select it as the period. This explains the look of your histogram. In your case, the bootstrap samples are most likely to select 1.372094d as the period, but also have a good chance to select 1.372105d. The values in between instead have a very low probability of being selected as the period.