# Improving the Accuracy of Planet Occurrence Rates from Kepler using Approximate Bayesian Computation

## TL;DR

This paper introduces a novel Bayesian framework using Approximate Bayesian Computation to improve the estimation of planet occurrence rates from Kepler data, especially for small planets in habitable zones.

## Contribution

The study develops a hierarchical Bayesian model with ABC and sequential importance sampling to more accurately estimate planet occurrence rates, surpassing traditional inverse detection efficiency methods.

## Key findings

- Increased occurrence rates for small planets at larger orbital periods.
- Estimated habitable zone planet occurrence rate density of 1.6^{+1.2}_{-0.5}.
- Identified a local minimum in occurrence rate between 1.5 and 2 R_earth.

## Abstract

We present a new framework to characterize the occurrence rates of planet candidates identified by Kepler based on hierarchical Bayesian modeling, Approximate Bayesian Computing (ABC), and sequential importance sampling. For this study we adopt a simple 2-D grid in planet radius and orbital period as our model and apply our algorithm to estimate occurrence rates for Q1-Q16 planet candidates orbiting around solar-type stars. We arrive at significantly increased planet occurrence rates for small planet candidates ($R_p<1.25 R_{\oplus}$) at larger orbital periods ($P>80$d) compared to the rates estimated by the more common inverse detection efficiency method. Our improved methodology estimates that the occurrence rate density of small planet candidates in the habitable zone of solar-type stars is $1.6^{+1.2}_{-0.5}$ per factor of 2 in planet radius and orbital period. Additionally, we observe a local minimum in the occurrence rate for strong planet candidates marginalized over orbital period between 1.5 and 2$R_{\oplus}$ that is consistent with previous studies. For future improvements, the forward modeling approach of ABC is ideally suited to incorporating multiple populations, such as planets, astrophysical false positives and pipeline false alarms, to provide accurate planet occurrence rates and uncertainties. Furthermore, ABC provides a practical statistical framework for answering complex questions (e.g., frequency of different planetary architectures) and providing sound uncertainties, even in the face of complex selection effects, observational biases, and follow-up strategies. In summary, ABC offers a powerful tool for accurately characterizing a wide variety of astrophysical populations.