rejects lots of samples if you infer jitter

[benjaminpope]

Hi Adrian,

On a particular HIRES dataset (which I can send you) which is a jittery M dwarf I try three samplers:

params_trend = JokerParams(P_min=0.5u.day, P_max=10.u.day,jitter=(np.log(5.2), 0.5), jitter_unit=u.m/u.s) params_trend = JokerParams(P_min=0.5u.day, P_max=10.u.day,jitter=(np.log(5.2), 0.01), jitter_unit=u.m/u.s) params_trend = JokerParams(P_min=0.5u.day, P_max=10.u.day,jitter=5*u.m/u.s)

with

samples_trend = joker.rejection_sample(data, n_prior_samples=2**20)

The first samples very badly, getting one (one!) good sample. The middle one, where we have a ridiculously tight prior on 5 m/s, gets a pretty good return on investment of 12616 good samples, and setting jitter explicitly gets a healthy 21767.

It doesn't seem reasonable to me that even a fairly moderate prior widtih rejects so overwhelmingly large a number of solutions... am I wrong or is there something amiss with the normalization of the jitter term or something?

All the best,

Ben

[adrn]

I'll take a look! Would you mind sending me the data? I will delete after this experiment in case there are data sharing issues :)

[adrn]

Hm, I do see the same thing, but I don't have a great answer for you! My guess would be that the data don't have a clear Keplerian signal, so the jitter prior tries to pull the jitter value to 0, but then it doesn't find a good orbital solution for the data, so few samples get returned? When the jitter prior is tight around 5 m/s, it allows more flexibility with the fits, so many more samples are returned. Here are the jitter values returned from your cases 1 (blue) and 2 (orange) - see in case 1 the jitter values for the returned samples are small:

[benjaminpope]

Weird - even setting a very wide prior I don't get anything very good.

50% of cadences are followed by one a day later, and 25% by another one a day after that - so I imagine we are at ~ mean Nyquist for ~ 2 days, though the shortest separations would give much shorter periods. I wonder if we have any sampling problems due to aliasing (164 epochs over 16 years is pretty irregular!).

On Thu, Feb 28, 2019 at 5:06 PM Adrian Price-Whelan < notifications@github.com> wrote:

Hm, I do see the same thing, but I don't have a great answer for you! My guess would be that the data don't have a clear Keplerian signal, so the jitter prior tries to pull the jitter value to 0, but then it doesn't find a good orbital solution for the data, so few samples get returned? When the jitter prior is tight around 5 m/s, it allows more flexibility with the fits, so many more samples are returned. Here are the jitter values returned from your cases 1 (blue) and 2 (orange) - see in case 1 the jitter values for the returned samples are small:

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[adrn]

I take from this that you expect there to be a signal in there?

[benjaminpope]

Not necessarily - but we want to robustly infer the stellar jitter and put upper limits on K for any short period planets. We expect a non detection but a rigorous one. On Thu, 28 Feb 2019 at 6:02 pm, Adrian Price-Whelan < notifications@github.com> wrote:

I take from this that you expect there to be a signal in there?

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[adrn]

Got it! OK then I think the only thing you can do is (a) go to many more samples, and (b) try a few different jitter priors. I'll put together a little demo notebook for what I would recommend trying and send it your way!

[benjaminpope]

Thanks!

On Fri, Mar 1, 2019 at 8:18 AM Adrian Price-Whelan notifications@github.com wrote:

Got it! OK then I think the only thing you can do is (a) go to many more samples, and (b) try a few different jitter priors. I'll put together a little demo notebook for what I would recommend trying and send it your way!

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-- Dr Benjamin Pope NASA Sagan Fellow Center for Cosmology and Particle Physics New York University 726 Broadway New York, NY 10003