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Abstract:
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The Kepler Mission has found thousands of planetary candidates with radii between 1 and 4 earth radius. These planets have no analogues in our Solar System, providing an unprecedented opportunity to understand the distribution of planetary compositions allowed by planet formation and evolution. In this article we infer about the thermal evolution of the hydrogen-helium envelope around the rocky core using the data on the transit depth of such planets. Lopez and Fortney (2002) studied the relationship between the radius of the planet and their mass, fractional envelope of hydrogen-helium, host star radius and stellar flux using a deterministic model (Lop 14) based on astrophysical theory. Wolfgang and Lopez (2015) have used a Bayesian hierarchical model where the expensive Lop 14 model was executed several thousand times to sample from the posterior. Here we use Gaussian process to emulate the Lop 14 model from the existing runs of the simulator. The Gaussian process emulator would be inexpensive and would also incorporate the model uncertainty. Such emulator model is different than the traditional one as the emulator output, the planet radius, is itself an unknown random quantity.
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