A Nonparametric Correlation and Causation Inference of a Peru Margin Multi-proxy Holocene Record
Abstract
Paleoclimate proxies are correlated with climate events and it is common to reconstruct a series of past climate events based on the associated proxies. Moreover, analyzing multiple proxies gathered at the same location leads to a comprehensive reconstruction of the related events, depending on their correlation and causation. Two obstacles, however, make examination of the relationship between multiple proxies difficult: 1) correlation and causation are often hard to be separated in the real data and 2) each proxy observation is not regularly spaced over ages in general and multiple proxies are usually not synchronized over time. [Ahn et al. (2020)] overcome the second obstacle by first arranging proxies regularly and then filling in missing observations with a Kalman filter, and then challenge the first obstacle with an autoregressive hidden Markov model, to analyze four proxies (SST, C37, 15N and %N) from the site MW8708-PC2. However, rearranging and filtering data usually result in the loss of information and Markov models often ignore long-term dependencies across data. Here, we present a nonparametric correlation and causation inference based on a multi-task Gaussian process state-space model, which brings four advantages as follows: 1) the multi-task Gaussian process state-space model takes both evenly and unevenly spaced data so it does not need data rearrangement or filtering, 2) the model is nonparametric so does not rely on parametric assumptions, 3) correlation and causation are simultaneously inferred in the forms of an estimated correlation matrix and a lead-or-lag analysis, respectively, and 4) the model is free from the Markovian assumption, thus it can capture long-term effects between multiple proxies. Our multi-task Gaussian process state-space model is applied to the raw four proxy data (SST, C37, 15N and %N) over the Holocene epoch (0.60 9.44 ka BP) at site MW8708-PC2 (central Peru margin) and successfully obtains their regression models, correlation matrix, and relative lead and lags. The covariance kernel suggests that the dependency over ages last for more than 250 years. The correlation matrix is consistent with [Ahn et al. (2020)]. Posterior distributions of relative lead and lags that SST, C37 and %N are similar while 15N is preceded by them are consistent with the origins of proxies.
- Publication:
-
AGU Fall Meeting Abstracts
- Pub Date:
- December 2021
- Bibcode:
- 2021AGUFMPP11B..04L