Technique for folding sparse event data in order to detect an underlying periodicity? @JamesK's answer to When will the next transit of Earth be visible from Mars? Was the last one really on May 11, 1984? lists dates of 18 transits which I've converted to days since 1500-Jan-01 as
[35011, 44319, 73176, 109885, 138742, 148050, 176908, 213616, 242474, 251782, 280639, 317347, 326656, 346205, 355514, 384371, 421078, 430388]

Answers to Why do transits of Earth across the Sun seen from Mars follow a pattern of occurring after 26, 79 then 100 years? explain why this happens and why if they happen at all, the happen in May and November.
As an exercise I'd like to use folding to see if I can detect those or similar periodicities in addition to the 6 month periodicity.
I could

for each period of N days recalculate those modulo N
histogram the results

but since there are so few event, they rarely occur when their time comes, and so many days between events, there won't be obvious peaks in the resulting histogram.
Question: Is there a technique for folding sparse event data in order to detect an underlying periodicity?

Events convoluted with σ=1000 day gaussians purely for illustration purposes. I thought about applying some Fourier transform to this but I don't think that that makes sense, and would be cheating rather than folding.
While this is not exactly how folding works, one-dimensional data encourages trying some simple statistical tallying first.

What very easily reveals those periodicities is just tallying up the deltas, with an appropriate fuzziness for what periodicities are relevant:

Deltas

[0, 9308, 28857, 36709, 28857, 9308, 28858, 36708, 28858, 9308, 28857, 36708, 9309, 19549, 9309, 28857, 36707, 9310]
Already here, some patterns should be apparent. But we have some extra information that could be used to filter out the short period noise.

Rounding at an appropriate sampling frequency

Earth transits aren't going to happen every day. If there was an Earth transit yesterday, it can't happen again today, or next day, or even the next month. In fact, we know they can only happen once for every synodic period of Mars-Earth (780 days).
To not miss out in any &quot;legitimate&quot; part of the signal, we should sample at at least twice of that rate. &quot;one year&quot; happens to be pretty close to half of 780 days.
The periodicity is then readily visible:
[26, 79, 101, 79, 26, 79, 101, 79, 26, 79, 101, 26, 54, 26, 79, 101, 26]
Which also reveals an even higher extra periodicity of about 206 years.
With a strong 206 year periodicity found in a set of events only covering a little over 400 years, there's not enough data to with any certainty detect any higher order periodicities that that.