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A coarse Bayesian approach to evaluate luminescence ages

Zink A.

Geochronometria

2013

Vol. 40, no. 2

90--100

This paper develops a simplified Bayesian approach to evaluate a luminescence age. We limit our purpose to the cause-effect relationship between the age and the accumulated dose. The ac-cumulated dose is given as a function of the age and several others parameters: internal radionuclides contents, gamma dose rate, cosmic dose rate, alpha efficiency, wetness, conversion factors, wetness coefficients, fading rate and storage time. The age is the quantity we are looking for. Bayes’ theorem expresses the changes on the probability distribution of age due to the luminescence study. The in-formation before study (prior) comprises what is previously known about the age and the archaeolog-ical model (cultural period, stratigraphic relations, type, etc.) as well as the parameters of the physical model. The accumulated dose consists in the data describing the measurement. The various stages of Bayesian approach were implemented using the software WinBugs. Simulated data sets were used in various models. We present various small models representing typical exam-ples encountered in luminescence dating.

Chemical U-Th-Pb geochronology: a precise explicit approximation of the age equation and associated errors

Săbău G.

Geochronometria

2012

Vol. 39, no. 3

167-179

In a single decaying system, the age determined from the exponential decay law is directly related to its linear Maclaurin approximation. This relationship can be additively extended to several decaying systems resulting in the same daughter element, by using proportionality functions, thus al-lowing an explicit formulation of the age as a function of element concentrations. The values of the binary proportionality function for the238U- 238U-Pb system and the ternary proportionality function for the 232Th-238U-235-U-Pb system were determined by iterations of the exponential decay formula up to 4 Ga, with a step of 10 Ma, for a set of 24 different U/Th ratios. From the iteration data, the expressions of the two functions and the associated coefficients were determined by polynomial regression and mathematical programing on conveniently separated time and compositional intervals. Additional time- and composition-dependent age corrections optimized by mathematical program-ming of the residuals lead to an accuracy of 0.005 Ma of the resulting age. The error propagation can be traced through all the operations defined by explicit formulas according to simple error propaga-tion rules, finally allowing the calculation of the standard error of the result. The formulas and param-eters derived can be used in a calculation spreadsheet.