colej / okapy

Routines for drawing inference on orbital parameters from radial velocity measurements.

okapy

Routines for drawing inference on orbital parameters from radial velocity measurements. ** Overview **

First, you need to create a conda environment with the hmc_rv_modelling.yml file provided. --> You need to change two things in this: --> First, you CAN change the name at the top of the file --> Second, you MUST change the path at the bottom of the file to lead to where you store the rest of your conda environments

--> To install the environment, simply run: --> conda env create --file hmc_rv_modelling.yml --> To enter environment, run: --> source activate NAME

To actually run the code, you'll need to place it in its own directory, i.e. rv_hmc_modelling The code assumes a particular sub-directory structure to organize the data, config files, solution files, etc. The structure is as follows:

• rv_hmc_modelling/ -> hmc_rv_v07.py -> configs/ # This is where you put the configuration files -> data/ # This is where you put the data -> solns/ # This is where the code dumps the output and plots

** Config files **

Great! Now let's take a look at an example Configuration file. These are stored as YAML files. The file will have a few required inputs, and I'm working on adding some features in the meantime. But, for now, there are three sections: 1) general, 2) varpars, and 3) priors.

1. general - contains general information about paths and values used to format the save strings. It also contains information used to configure the NUTS sampler, such as the number of chains, draws, and tuning samples. In general, these numbers should work fairly well, however, if you want to increase these values, feel free! That being said, the computation time scales quite quickly with these values.

   • The target parameter should never be set below 0.9.
   • There are numerous settings to handle the eccentricity. For small eccentricities, ecc_type: small is a good choice because of how the code samples from a half-cauchy distribution for the value of ecc. Alternatively, you can sample sqrt(e)cos(omega) and sqrt(e)sin(omega) from a uniform disc using ecc_type: disc or you can sample ecc and omega directly from uniform distributions using ecc_type: normal. Finally, you can force a circular orbit using: ecc_type: circular.
   • This will assume SB1 as long as secondary_obs: None is set. To use an SB2 setup, just put a path to the data file. ** You will also need to include a section for k2 under the varpars section. **

2. varpars - these are the parameters that will be fit during the modelling. Try to put the values per variable reasonably close to what you think they should be, otherwise the MAP algorithm could struggle. The prior argument should be the name of a distribution within pymc. The parameter values are sampled from this distribution. There is also the option to transform the scale of the data. If transform: None is set, then the distribution is sampled linearly. If transform: log and prior: Uniform, then the variable will be sampled from a uniform distribution in log-space. Similarly, you can set prior: Normal and transform: None to apply a strict Gaussian prior. The values of kwargs should be able to be passed to the distribution. For instance, Uniform priors will always have lower and upper arguments, whereas Normal priors require mu and sigma as arguments. A sensible value for testval needs to be set for all variables.

3. priors - effectively a place-holder for the time being, so don't worry about these!

general: path: ./ prefix: v772Cas iter: i01 primary_obs: data/v772Cas_primary_RVs.dat secondary_obs: None chains: 2 cores: 4 draws: 1000 tune: 1000 target: 0.97 type: rv ecc_type: small varpars: Period: prior: Uniform transform: log kwargs: testval: 5.01370 lower: 4.8 upper: 5.2 Gamma: prior: Uniform transform: None kwargs: testval: 0. lower: -100. upper: 100. K1: prior: Uniform transform: log kwargs: testval: 60.5 lower: 1. upper: 400 priors: ecc: mean: 0. std: 0.4 omega: mean: 3.14 std: 0.1

** Running the code **

Running the code is very simple. Just issue: --> python3 hmc_rv_v0X.py configs/hd165246.yaml

It will tell you what its doing along the way. First, it has to instantiate the model and all of its symbolic links in pymc3. Then, it will perform an initial Maximum a-posteriori (MAP) optimisation and return the best model. A plot will appear for the MAP solution.

Next, it will use the MAP solution as the starting point to initialise the NUTS Hamiltonian Monte Carlo sampling algorithm. After it runs, it will throw away the tuning samples and marginalize over the remaining samples to produce our posteriors. A plot of the binned posteriors will pop up and save, followed by a plot of the best model from the sampling and its 16 & 84 percentile models. The best parameters and plots are saved in the soln folder.