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

Danley C. Hsu, Eric B. Ford, Darin Ragozzine, Robert C. Morehead

Research output: Contribution to journalArticle

12 Citations (Scopus)

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 2D grid in planet radius and orbital period as our model and apply our algorithm to estimate occurrence rates for Q1-Q16 planet candidates orbiting solar-type stars. We arrive at significantly increased planet occurrence rates for small planet candidates (R p < 1.25 R ) at larger orbital periods (P > 80 day) compared to the rates estimated by the more common inverse detection efficiency method (IDEM). Our improved methodology estimates that the occurrence rate density of small planet candidates in the habitable zone of solar-type stars is 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 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.

Original languageEnglish (US)
Article number205
JournalAstronomical Journal
Volume155
Issue number5
DOIs
StatePublished - May 2018

Fingerprint

planets
planet
occurrences
orbitals
astrophysics
rate
stars
radii
false alarms
forward modeling
estimates
sampling
grids
methodology
acoustics
modeling

All Science Journal Classification (ASJC) codes

  • Astronomy and Astrophysics
  • Space and Planetary Science

Cite this

@article{d24f8b134dfa443e9ccfeb76b514c32c,
title = "Improving the Accuracy of Planet Occurrence Rates from Kepler Using Approximate Bayesian Computation",
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 2D grid in planet radius and orbital period as our model and apply our algorithm to estimate occurrence rates for Q1-Q16 planet candidates orbiting solar-type stars. We arrive at significantly increased planet occurrence rates for small planet candidates (R p < 1.25 R ⊕) at larger orbital periods (P > 80 day) compared to the rates estimated by the more common inverse detection efficiency method (IDEM). Our improved methodology estimates that the occurrence rate density of small planet candidates in the habitable zone of solar-type stars is 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 ⊕ 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.",
author = "Hsu, {Danley C.} and Ford, {Eric B.} and Darin Ragozzine and Morehead, {Robert C.}",
year = "2018",
month = "5",
doi = "10.3847/1538-3881/aab9a8",
language = "English (US)",
volume = "155",
journal = "Astronomical Journal",
issn = "0004-6256",
publisher = "IOP Publishing Ltd.",
number = "5",

}

Improving the Accuracy of Planet Occurrence Rates from Kepler Using Approximate Bayesian Computation. / Hsu, Danley C.; Ford, Eric B.; Ragozzine, Darin; Morehead, Robert C.

In: Astronomical Journal, Vol. 155, No. 5, 205, 05.2018.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Improving the Accuracy of Planet Occurrence Rates from Kepler Using Approximate Bayesian Computation

AU - Hsu, Danley C.

AU - Ford, Eric B.

AU - Ragozzine, Darin

AU - Morehead, Robert C.

PY - 2018/5

Y1 - 2018/5

N2 - 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 2D grid in planet radius and orbital period as our model and apply our algorithm to estimate occurrence rates for Q1-Q16 planet candidates orbiting solar-type stars. We arrive at significantly increased planet occurrence rates for small planet candidates (R p < 1.25 R ⊕) at larger orbital periods (P > 80 day) compared to the rates estimated by the more common inverse detection efficiency method (IDEM). Our improved methodology estimates that the occurrence rate density of small planet candidates in the habitable zone of solar-type stars is 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 ⊕ 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.

AB - 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 2D grid in planet radius and orbital period as our model and apply our algorithm to estimate occurrence rates for Q1-Q16 planet candidates orbiting solar-type stars. We arrive at significantly increased planet occurrence rates for small planet candidates (R p < 1.25 R ⊕) at larger orbital periods (P > 80 day) compared to the rates estimated by the more common inverse detection efficiency method (IDEM). Our improved methodology estimates that the occurrence rate density of small planet candidates in the habitable zone of solar-type stars is 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 ⊕ 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.

UR - http://www.scopus.com/inward/record.url?scp=85047296434&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85047296434&partnerID=8YFLogxK

U2 - 10.3847/1538-3881/aab9a8

DO - 10.3847/1538-3881/aab9a8

M3 - Article

AN - SCOPUS:85047296434

VL - 155

JO - Astronomical Journal

JF - Astronomical Journal

SN - 0004-6256

IS - 5

M1 - 205

ER -