The Bayesian Change Point and Variable Selection Algorithm: Application to the δ18O Proxy Record of the Plio-Pleistocene

Abstract

In this article, we introduce the Bayesian change point and variable selection algorithm that uses dynamic programming recursions to draw direct samples from a very high-dimensional space in a computationally efficient manner, and apply this algorithm to a geoscience problem that concerns the Earth's history of glaciation. Strong evidence exists for at least two changes in the behavior of the Earth's glaciers over the last five million years. Around 2.7 Ma, the extent of glacial cover on the Earth increased, but the frequency of glacial melting events remained constant at 41 kyr. A more dramatic change occurred around 1 Ma. For over three decades, the “Mid-Pleistocene Transition” has been described in the geoscience literature not only by a further increase in the magnitude of glacial cover, but also as the dividing point between the 41 kyr and the 100 kyr glacial worlds. Given such striking changes in the glacial record, it is clear that a model whose parameters can change through time is essential for the analysis of these data. The Bayesian change point algorithm provides a probabilistic solution to a data segmentation problem, while the exact Bayesian inference in regression procedure performs variable selection within each regime delineated by the change points. Together, they can model a time series in which the predictor variables as well as the parameters of the model are allowed to change with time. Our algorithm allows one to simultaneously perform variable selection and change point analysis in a computationally efficient manner. Supplementary materials including MATLAB code for the Bayesian change point and variable selection algorithm and the datasets described in this article are available online or by contacting the first author.