A Unified Bayesian Study of Exoplanet Populations: From Survey Biases to Circumbinary Systems in Kepler and TESS

Since the 1990s, the number of exoplanets—celestial worlds orbiting stars outside of our solar system—has increased dramatically, producing an abundance of fresh data. Using data from the NASA Exoplanet archive, Kepler, and TESS surveys to generate a single dataset, this paper gives a statistical analysis of exoplanet occurrence and the properties of their host stars. Two hierarchical models—Bayesian and Poisson—are employed in a Bayesian regression framework to evaluate the relationship between planet occurrence and star parameters such metallicity, effective temperature, mass, and radius.,A comparison of statistical formulations is made possible by the evaluation of model performance, which incorporates information criteria and posterior predictive tests. For meaningful comparisons between Kepler and TESS data, the analysis includes detection efficiency corrections to account for observational biases inherent in various survey methodologies, such as transit and radial velocity detections. By incorporating mass-radius connections and classifying planets as super-Earths, sub-Neptunes, or giant planets, the study differentiates planetary populations. It then expands to circumbinary systems and evaluates the impact of star multiplicity on planet occurrence.,Significantly, an empirical scaling relationship between planetary radius and star properties is shown, demonstrating that this scaling is survey-dependent and especially robust in TESS data. Furthermore, the core accretion concept is supported by a positive association between planetary mass and star metallicity. The work highlights the influence of selection effects from survey approaches on population estimates and finds substantial predictive correlations between host star attributes and planet occurrence.,Overall, this work offers a reproducible framework for exoplanet analysis, emphasizing Bayesian inference while enhancing understanding through an interactive dashboard for astronomers to explore exoplanet data and their host stars comprehensively.