Probabilistic Generative Models for the Statistical Inference of Unobserved Paleoceanographic Events: Application to Stratigraphic Alignment for Inference of Ages

The broad goal of this presentation is to demonstrate the utility of probabilistic generative models to capture investigators’ knowledge of geological processes and proxy data to draw statistical inferences about unobserved paleoclimatological events. We illustrate how this approach forces investigators to be explicit about their assumptions, and about how probability theory yields results that are a mathematical consequence of these assumptions and the data. We illustrate these ideas with the HMM-Match model that infers common times of sediment deposition in two records and the uncertainty in these inferences in the form of confidence bands. HMM-Match models the sedimentation processes that led to proxy data measured in marine sediment cores. This Bayesian model has three components:

1) a generative probabilistic model that proceeds from the underlying geophysical and geochemical events, specifically the sedimentation events to the generation the proxy data

Sedimentation ---> Proxy Data

; 2) a recursive algorithm that reverses the logic of the model to yield inference about the unobserved sedimentation events and the associated alignment of the records based on proxy data

Proxy Data ---> Sedimentation (Alignment)

; 3) an expectation maximization algorithm for estimating two unknown parameters.

We applied HMM-Match to align 35 Late Pleistocene records to a global benthic d¹⁸Ostack and found that the mean width of 95% confidence intervals varies between 3-23 kyr depending on the resolution and noisiness of the core’s d¹⁸O signal. Confidence bands within individual cores also vary greatly, ranging from ~0 to >40 kyr. Results from this algorithm will allow researchers to examine the robustness of their conclusions with respect to alignment uncertainty. Figure 1 shows the confidence bands for one low resolution record.