I think maybe there are some \ref{} issues; there are experiments and there are section numbers, but these aren't the same.

To keep track of units, transform to / from emcee sampling parameters (e.g., e,\omega <=> \sqrt{e},\cos\omega, \sqrt{e},\sin\omega)

cyan SUCKS

• these outputs are perfect inputs for a hierarchical model (see DFM; Hogg)
• even very poor observations might strongly constrain a hierarchical model (as per Rix email)

And Bedell

We should cite his DNEST but ALSO cite his paper (he has one, I think) on exoplanet RV inference.

We should make a comment that we actually have a prior belief about v0 even though we don't impose it -- if disk star, v0 ~ N(0,30) km/s; halo star, v0 ~ N(0,150) km/s, etc.

A slightly more general version is:

"The Joker: A custom Monte Carlo sampler for periodic radial velocity data"

but that is boring as hell and doesn't catch the eye as well as explicitly mentioning binary stars and exoplanets. I don't have a strong opinion, but want to raise the point for discussion.

Can we do a good case that is effectively unimodal as well?

Just sayin'

Add words to the Discussion talking about incorporating more linear parameters into the model.

OK, not exactly, but we need to add more words to the intro and discussion to explain why this is more desirable than using DNest. We want to explicitly state that you don't have to do any 2nd order tests of your samples to try to assess whether you are converged / have a true sampling from the posterior pdf. Starting with a dense enough (define) prior sampling, if The Joker returns many samples, you "just know" that you are done.

This is a mpl bug, but let's fix it

They always look uniform, like the prior...

Hash on something like (re-run number, worker rank / chunk index)

• Experiment 1: generate fake data with e=0.643, P=100.09 day, asini = 0.42 R_sun (or some reasonable set of parameters with high eccentricity) - 4 observation times uniformly sampled in a ~3 year window
• Experiment 2: (what is currently Experiment 1) Run on a Troup star with few observations
• Experiment 3: (what is currently Experiment 2) Run on a Troup star with many observations, downsample successively. Highlight switchover to emcee
• Experiment 4: Run with full set of observations from Experiment 3 with uncertainties * [2,4,8,16]
• Experiment 5: motivated by the fact that some data points seem to carry a lot of information (demonstrated in Exp 3), repeat analysis from Experiment 1, but move the observation time of data point 4 through 1 cycle in period (in 8 steps). At certain phases, this point is very informative - we can use our tools to develop scheduling priorities.

• give him a paper-and-pen proof, by sms, and
• equation (1) makes no reference to P or phi_0, so give a second equation that gives f in terms of these.

In the discussion we should raise the issue that if you have (a) crappy, sparse data, or (b) a lot of good quality data, and all you want to do is learn about the system, you don't need to start with so many prior samples (many will pass the rejection step). It's really the intermediate regime where it is important.

But, if you want to do hierarchical modeling, or if you want to assess whether or not your posterior is multi-modal, you need to sample the hell out of your priors.

Technically, the posterior will always be multimodal. All we are asking for is effective unimodality. This requires an audit of the text

because in general, for exoplanets, our dumb noise model won't be good enough.

Add some conclusions to each experiment because the discussion section is too late!

Experiment 1 - we do get samples at truth, yes more weight at short periods, but we're actually sampling.

No good deed goes unpunished.

The instructions are (telegraphically) in the method section of the paper.

Right now run-sampler.py generates new batches of prior samples each time it is run because it only takes minutes (low incentive to optimize). But for the experiments, I should just generate a massive file of samples and use chunks of the same samples for all experiments.

... in my bw print out of figs 1 4 8

Switch to using velocity semi-amplitude, but still put prior on asini

This requires some text changes as well.

TriggerWarning

copy the relevant part of the peerless latex header

The latex labels for the parameter names should automatically add the units, not hard-set like they are now.

latex_labels = [r'$\ln (P/{\rm day})$', '$e$', r'$\omega$ [deg]', r'$\phi_0$ [deg]',
                's [m s$^{-1}]$', r'$K$ [m s$^{-1}$]', '$v_0$ [km s$^{-1}$]']

I MUCH prefer M

This project is also relevant for supermassive black hole binary searches and population inference:

https://ui.adsabs.harvard.edu/#abs/2016arXiv160401020C/abstract
https://ui.adsabs.harvard.edu/#abs/2015MNRAS.453.1562G/abstract

they look like hell! Self-assigning.

Like the software tag, there is a facilities tag, which should say sdss-iii or apogee

...or in fact before every \section{}. The idea behind this issue is to clear all the floats before we discuss.

I want a parameter s-squared, such that the noise variances become

sigma^2 + s-squared

This has to be sampled along with the other non-linear parameters, so we have to go to 5-d sampling (and probably 2 ** 29 samples).

Put a prior on s-squared that is Gaussian in the LOG of s-squared.

@adrn, can you try doing this and see if everything still works? I only ask because all our customers want this.

• make a decision
• make sure the code and text both reflect this decision
• cite the correct literature

We could make data with ZERO signal, and then:

• analyze it straightforwardly and correctly, to see what a "null" looks like
• analyze it in the case that we have accidentally underestimated the error bars by a factor of three!

In the latter case, we should find some kind of posterior pdf... What?

(Hogg thinks: no)

When plotting Troup's parameters over what we find in Experiments 2,3,4, the color for Troup should be different from plotting the True parameters for fake data in Experiments 1,5

There is a list at the top of the LaTeX file. This issue can be closed when that list is empty.