Segmenting geochemical records using hierarchical probabilistic models

Abstract

Geochemical records of drill cores can be complex and multi-variate. We address the problem of automatically classifying collections of sequential geochemical data. Our approach uses a change-point analysis based on a probabilistic explanation of the binary segmentation method. Change-points, which separate geochemical data into segments of self-similar trends, are accepted only if they increase the global probability of the data set. Increased model complexity is penalised by an Occam factor that offsets improvements in explaining the data trends. Therefore, simpler models are preferred. The method is insensitive to unequally spaced samples in the geochemical records, negating the need to interpolate data for missing values. Probability analysis requires an estimation of variance in the measured data which affects our ability to detect change-points. Extension of change-point analysis to multiple variables in geochemical data sets is straightforward. Typical classification schemes only segment geochemical data into regions that are explained by constant models: we extend our analysis to include models where chemical concentrations change linearly with depth. The recursive application of the binary segmentation algorithm generates hierarchical models that can be used to classify geochemical records over a variety of distance scales.We provide a clear explanation of the development of the mathematics of change-point analysis with binary segmentation and demonstrate its utility with a suite of examples. We compare our results to published classification methods, and provide two examples of classification on data sets from peat bogs and drill core. In one example we detect linear trends in concentrations of Ti, Cr, and Zr that would not be detected with other methods.