Bayesian Methods for Analysis and Adaptive Scheduling of Exoplanet Observations

TL;DR

This paper presents Bayesian data analysis tools for exoplanet detection, orbit estimation, and adaptive observation scheduling, addressing complex nonlinear models and multimodal likelihood functions in stellar reflex motion data.

Contribution

It introduces novel Bayesian methods and adaptive sampling techniques tailored for analyzing nonlinear, multimodal models in exoplanet research, improving detection and scheduling accuracy.

Findings

Effective Bayesian analysis of stellar reflex motion data.

Adaptive MCMC and importance sampling improve inference.

Framework supports multi-planet systems and various motion types.

Abstract

We describe work in progress by a collaboration of astronomers and statisticians developing a suite of Bayesian data analysis tools for extrasolar planet (exoplanet) detection, planetary orbit estimation, and adaptive scheduling of observations. Our work addresses analysis of stellar reflex motion data, where a planet is detected by observing the "wobble" of its host star as it responds to the gravitational tug of the orbiting planet. Newtonian mechanics specifies an analytical model for the resulting time series, but it is strongly nonlinear, yielding complex, multimodal likelihood functions; it is even more complex when multiple planets are present. The parameter spaces range in size from few-dimensional to dozens of dimensions, depending on the number of planets in the system, and the type of motion measured (line-of-sight velocity, or position on the sky). Since orbits are periodic, Bayesian generalizations of periodogram methods facilitate the analysis. This relies on the model being linearly separable, enabling partial analytical marginalization, reducing the dimension of the parameter space. Subsequent analysis uses adaptive Markov chain Monte Carlo methods and adaptive importance sampling to perform the integrals required for both inference (planet detection and orbit measurement), and information-maximizing sequential design (for adaptive scheduling of observations). We present an overview of our current techniques and highlight directions being explored by ongoing research.