Statistical models for mixed fission track ages

Abstract

In fission track analysis it is common to find that the true ages of different crystal grains vary within a sample, and this may be important for geological interpretation. There are at least two well-recognized geological processes that lead to mixed ages: grains from multiple sources, and differential annealing between grains of differing composition. Data from multiple sources may be represented statistically by a finite mixture model, usually with two or three components, but data arising from the multicompositional annealing process may be better modelled as an infinite mixture. We discuss finite mixtures and two new infinite mixture models: a random effects model whose parameters describe the location and spread of the population grain ages, and a more general model encompassing both two-component mixtures and random effects. We illustrate with case studies how to use these models to estimate various features of interest such as the minimum age, the other component ages and the age dispersion.