Quantifying comparison of large detrital geochronology data sets

Abstract

The increase in detrital geochronological data presents challenges to existing approaches to data visualization and comparison, and highlights the need for quantitative techniques able to evaluate and compare multiple large data sets. We test five metrics commonly used as quantitative descriptors of sample similarity in detrital geochronology: the Kolmogorov-Smirnov (K-S) and Kuiper tests, as well as Cross-correlation, Likeness, and Similarity coefficients of probability density plots (PDPs), kernel density estimates (KDEs), and locally adaptive, variable-bandwidth KDEs (LA-KDEs). We assess these metrics by applying them to 20 large synthetic data sets and one large empirical data set, and evaluate their utility in terms of sample similarity based on the following three criteria. (1) Similarity of samples from the same population should systematically increase with increasing sample size. (2) Metrics should maximize sensitivity by using the full range of possible coefficients. (3) Metrics should minimize artifacts resulting from sample-specific complexity. K-S and Kuiper test p-values passed only one criterion, indicating that they are poorly suited as quantitative descriptors of sample similarity. Likeness and Similarity coefficients of PDPs, as well as K-S and Kuiper test D and V values, performed better by passing two of the criteria. Cross-correlation of PDPs passed all three criteria. All coefficients calculated from KDEs and LA-KDEs failed at least two of the criteria.