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

Grethe Hystad, Ahmed Eleish, Robert M. Hazen, Shaunna M. Morrison, Robert T Downs

Research output: Contribution to journalArticle

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 languageEnglish (US)
JournalMathematical Geosciences
DOIs
StatePublished - Jan 1 2019

Fingerprint

Noninformative Prior
Bayesian Estimation
Poisson distribution
population size
Population Size
Estimate
Log Normal Distribution
Generalized Inverse
planet
statistical distribution
Markov Chain Monte Carlo Simulation
Bayes Estimate
mineral
Markov chain
Inverse Model
Empirical Bayes
Rare Events
Statistical Distribution
Bayesian Methods
relative abundance

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

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

In: Mathematical Geosciences, 01.01.2019.

Research output: Contribution to journalArticle

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