Mixture modeling of multi-component data sets with application to ion-probe zircon ages

Details Mixture modeling of multi-component data sets with application to ion-probe zircon ages Mixture modeling of multi-component data sets with application to ion-probe zircon ages

Dec 1994

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1994e%26psl.128..373s&link_type=abstract

Earth and Planetary Science Letters (ISSN 0012-821X), vol. 128, no. 3-4, p. 373-390

Statistics

Methodology

47

Ellipses, Geochronology, Ion Probes, Rocks, Statistical Analysis, Zirconium, Error Functions, Laser Fusion, Mathematical Models, Normal Density Functions

Scientific paper

A method is presented for detecting multiple components in a population of analytical observations for zircon and other ages. The procedure uses an approach known as mixture modeling, in order to estimate the most likely ages, proportions and number of distinct components in a given data set. Particular attention is paid to estimating errors in the estimated ages and proportions. At each stage of the procedure several alternative numerical approaches are suggested, each having their own advantages in terms of efficency and accuracy. The methodology is tested on synthetic data sets simulating two or more mixed populations of zircon ages. In this case true ages and proportions of each population are known and compare well with the results of the new procedure. Two examples are presented of its use with sets of SHRIMP U-238 - Pb-206 zircon ages from Palaeozoic rocks. A published data set for altered zircons from bentonite at Meishucun, South China, previously treated as a single-component population after screening for gross alteration effects, can be resolved into two components by the new procedure and their ages, proportions and standard errors estimated. The older component, at 530 +/- 5 Ma (2 sigma), is our best current estimate for the age of the bentonite. Mixture modeling of a data set for unaltered zircons from a tonalite elsewhere defines the magmatic U-238 - Pb-206 age at high precision (2 sigma +/- 1.5 Ma), but one-quarter of the 41 analyses detect hidden and significantly older cores.

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