Mathematical Geology

, Volume 20, Issue 6, pp 693–698 | Cite as

Bayesian estimation of isotopic age differences

  • Rane L. Curl
Articles

Abstract

Isotopic dating is subject to uncertainties arising from counting statistics and experimental errors. These uncertainties are additive when an isotopic age difference is calculated. If large, they can lead to no significant age difference by “classical” statistics. In many cases, relative ages are known because of stratigraphic order or other clues. Such information can be used to establish a Bayes estimate of age difference which will include prior knowledge of age order. Age measurement errors are assumed to be log-normal and a noninformative but constrained bivariate prior for two true ages in known order is adopted. True-age ratio is distributed as a truncated log-normal variate. Its expected value gives an age-ratio estimate, and its variance provides credible intervals. Bayesian estimates of ages are different and in correct order even if measured ages are identical or reversed in order. For example, age measurements on two samples might both yield 100 ka with coefficients of variation of 0.2. Bayesian estimates are 22.7 ka for age difference with a 75% credible interval of [4.4, 43.7] ka.

Key words

Bayes estimate dating credible interval stalagmite log-normal 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Gascoyne, M. 1978, Discussion of Harmon and Curl (1978a): Bull. Nat. Speleo. Soc., v. 40, p. 123.Google Scholar
  2. Guttman, I.; Wilkes, S. S.; and Hunter, J. S., 1982, Introductory Engineering Statistics: J. Wiley & Sons, New York, 580 p.Google Scholar
  3. Harmon, R. S. and Curl, R. L., 1978a, Preliminary Results on Growth Rate and Paleoclimate Studies of a Stalagmite from Ogle Cave, New Mexico: Bull. Nat. Speleo. Soc., v. 40, p. 25–26.Google Scholar
  4. Harmon, R. S. and Curl, R. L. 1978b, Reply to Gascoyne (1978): Bull Nat. Speleo. Soc., v. 40, p. 123–124.Google Scholar
  5. Latham, A. G.; Schwarz, H. P.; and Ford, D. C., 1986, The Paleomagnetism and U-Th Dating of Mexican Stalagmite, DAS2: Earth Planet. Sci. Lett., v. 79, p. 195–207.Google Scholar

Copyright information

© International Association for Mathematical Geology 1988

Authors and Affiliations

  • Rane L. Curl
    • 1
  1. 1.Department of Chemical EngineeringUniversity of MichiganAnn Arbor

Personalised recommendations