# Bayesian Model Comparisons in Planetary Science

#### Abstract

Model comparison in the modern era allows us to use statistical methods that were previously difficult with older machines. I present a state-of-the-art model comparison code that uses modern Bayesian statistics to measure the Bayes factor between two competing models. The Bayes factor is the ratio of the probability of the data given one model to the probability of the data given another model. My code was used to compare models in five problems in planetary science. The first three pertain to radial velocity exoplanet data. There is a degeneracy in the radial velocity exoplanet signal between a single planet on an eccentric orbit and a two-planet system with a period ratio of 2:1. This degeneracy could lead to misunderstandings of the dynamical histories of planetary systems as well as measurements of planetary abundances if the correct architecture is not established. We constrain the rate of mischaracterization by analyzing a sample of 60 non-transiting, radial velocity systems orbiting main sequence stars from the NASA Exoplanet Archive (NASA Archive) using my model comparison pipeline. We find that 15 systems (25% of our sample) show compelling evidence for the two-planet case with a confidence level of 95%. The Automated Planet Finder obtained additional data for seven of the best candidates. My pipeline finds that six of them continue to show strong evidence for the two-planet case. Observational strategies to break the 2:1 degeneracy are explored using two thousand synthetically generated single planets with eccentric orbits and two planets with circular orbits. We find that focusing on taking observations where the degeneracy is the weakest decreases the ambiguity between the models more than taking observations at random phases. The final two problems are model comparison of high-pressure/high–temperature experimental data. My code is able to identify two phase transitions in pressure-temperature water-ice data taken at Argonne National Lab in two separate datasets. One of the phase transitions found—cubic ice-VII to tetragonal ice-VII_t—is previously unreported until now. My code sees these phase transitions in X-ray diffraction data, which uses Bragg's law to peer into the crystal lattice of water, and in pressure–volume equation of state fits.

*This paper has been withdrawn.*