First, we are implementing a powerlaw parameterization for planet radius and period/insolation using the PyStan Nuts (the “No-U-Turn Sampler”) which optimizes HMC adaptively, in order to calculate occurrence rates based off of work by Chris Burke and the open science blog post by Dan Foreman-Mackey: The original exopop.ipynb from Dan Foreman-Mackey, is found at http://dan.iel.fm/downloads/notebooks/exopop.ipynb, and the accompanying blog post is at http://dan.iel.fm/posts/exopop/. Joe Catanzarite is co-investigator on this project and shares responsibility for the code development.

8/15/2016 This PyStan model version uses pre-computed completeness as input, for testing and development.

8/18/2016 We now have a working version of the power law occurrence rate model using PyStan that agrees with the results from the Burke calculations and the DFM python notebook blog post implementation. Now we will add radius uncertainties into the completeness calculations.

8/19/2016 Changing code back to radius/period.  Radius uncertainties now implemented.

8/22/2016 Code has a switch to select period or insolation, catalog version, stellar type.  

9/9/2016 Adding asymmetric planet radius uncertainties. 

TO DO:
- Full posteriors for the planet radii for catalog version 9.2
- GP bin height parameterization. 
- Stellar catalog uncertainties (e.g., Teff, Mass, Radius, etc.). 
- Reliability
- Multiplicity
- Interface with catalog 9.3, V1 occurrence rate products (e.g., completeness contours that are built from the 1-sigma depth function and numerical window function). 
- Explore other analysis models.