### Abstract

Recently, statistical distributions have been explored to provide estimates of the mineralogical diversity of Earth, and Earth-like planets. In this paper, a Bayesian approach is introduced to estimate Earth’s undiscovered mineralogical diversity. Samples are generated from a posterior distribution of the model parameters using Markov chain Monte Carlo simulations such that estimates and inference are directly obtained. It was previously shown that the mineral species frequency distribution conforms to a generalized inverse Gauss–Poisson (GIGP) large number of rare events model. Even though the model fit was good, the population size estimate obtained by using this model was found to be unreasonably low by mineralogists. In this paper, several zero-truncated, mixed Poisson distributions are fitted and compared, where the Poisson-lognormal distribution is found to provide the best fit. Subsequently, the population size estimates obtained by Bayesian methods are compared to the empirical Bayes estimates. Species accumulation curves are constructed and employed to estimate the population size as a function of sampling size. Finally, the relative abundances, and hence the occurrence probabilities of species in a random sample, are calculated numerically for all mineral species in Earth’s crust using the Poisson-lognormal distribution. These calculations are connected and compared to the calculations obtained in a previous paper using the GIGP model for which mineralogical criteria of an Earth-like planet were given.

Original language | English (US) |
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Journal | Mathematical Geosciences |

DOIs | |

State | Published - Jan 1 2019 |

### Fingerprint

### Keywords

- Bayesian statistics
- Mineral ecology
- Mineral frequency distribution
- Mixed Poisson distribution
- Species estimation

### ASJC Scopus subject areas

- Mathematics (miscellaneous)
- Earth and Planetary Sciences(all)

### Cite this

*Mathematical Geosciences*. https://doi.org/10.1007/s11004-019-09795-8

**Bayesian Estimation of Earth’s Undiscovered Mineralogical Diversity Using Noninformative Priors.** / Hystad, Grethe; Eleish, Ahmed; Hazen, Robert M.; Morrison, Shaunna M.; Downs, Robert T.

Research output: Contribution to journal › Article

*Mathematical Geosciences*. https://doi.org/10.1007/s11004-019-09795-8

}

TY - JOUR

T1 - Bayesian Estimation of Earth’s Undiscovered Mineralogical Diversity Using Noninformative Priors

AU - Hystad, Grethe

AU - Eleish, Ahmed

AU - Hazen, Robert M.

AU - Morrison, Shaunna M.

AU - Downs, Robert T

PY - 2019/1/1

Y1 - 2019/1/1

N2 - Recently, statistical distributions have been explored to provide estimates of the mineralogical diversity of Earth, and Earth-like planets. In this paper, a Bayesian approach is introduced to estimate Earth’s undiscovered mineralogical diversity. Samples are generated from a posterior distribution of the model parameters using Markov chain Monte Carlo simulations such that estimates and inference are directly obtained. It was previously shown that the mineral species frequency distribution conforms to a generalized inverse Gauss–Poisson (GIGP) large number of rare events model. Even though the model fit was good, the population size estimate obtained by using this model was found to be unreasonably low by mineralogists. In this paper, several zero-truncated, mixed Poisson distributions are fitted and compared, where the Poisson-lognormal distribution is found to provide the best fit. Subsequently, the population size estimates obtained by Bayesian methods are compared to the empirical Bayes estimates. Species accumulation curves are constructed and employed to estimate the population size as a function of sampling size. Finally, the relative abundances, and hence the occurrence probabilities of species in a random sample, are calculated numerically for all mineral species in Earth’s crust using the Poisson-lognormal distribution. These calculations are connected and compared to the calculations obtained in a previous paper using the GIGP model for which mineralogical criteria of an Earth-like planet were given.

AB - Recently, statistical distributions have been explored to provide estimates of the mineralogical diversity of Earth, and Earth-like planets. In this paper, a Bayesian approach is introduced to estimate Earth’s undiscovered mineralogical diversity. Samples are generated from a posterior distribution of the model parameters using Markov chain Monte Carlo simulations such that estimates and inference are directly obtained. It was previously shown that the mineral species frequency distribution conforms to a generalized inverse Gauss–Poisson (GIGP) large number of rare events model. Even though the model fit was good, the population size estimate obtained by using this model was found to be unreasonably low by mineralogists. In this paper, several zero-truncated, mixed Poisson distributions are fitted and compared, where the Poisson-lognormal distribution is found to provide the best fit. Subsequently, the population size estimates obtained by Bayesian methods are compared to the empirical Bayes estimates. Species accumulation curves are constructed and employed to estimate the population size as a function of sampling size. Finally, the relative abundances, and hence the occurrence probabilities of species in a random sample, are calculated numerically for all mineral species in Earth’s crust using the Poisson-lognormal distribution. These calculations are connected and compared to the calculations obtained in a previous paper using the GIGP model for which mineralogical criteria of an Earth-like planet were given.

KW - Bayesian statistics

KW - Mineral ecology

KW - Mineral frequency distribution

KW - Mixed Poisson distribution

KW - Species estimation

UR - http://www.scopus.com/inward/record.url?scp=85063214635&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85063214635&partnerID=8YFLogxK

U2 - 10.1007/s11004-019-09795-8

DO - 10.1007/s11004-019-09795-8

M3 - Article

JO - Mathematical Geosciences

JF - Mathematical Geosciences

SN - 1874-8961

ER -