Reconstruction of Spatio-Temporal Temperature from Sparse Historical Records Using Robust Probabilistic Principal Component Regression

• Activity Number: 406 - Spatio-Temporal Methods in Ecology and Epidemiology
• Type: Contributed
• Date/Time: Tuesday, August 1, 2017 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistics and the Environment
• Author(s): John Tipton* and Mevin Hooten and Simon Goring
• Companies: Colorado State University and Colorado State University and Department of Geography, University of Wisconsin
• Keywords: Probabilistic Principal Component Regression ; Paleoclimate ; Bayesian Hierarchical Mode ; Hierarchical Pooling ; Robust Regression ; Predictive Validation

Abstract

We reconstruct spatially-explicit temperature surfaces from sparse and noisy measurements recorded at historical United States military forts and other observer stations from 1820-1894. One common method for reconstructing paleoclimate from proxy data is principal component regression (PCR). We explore PCR in a Bayesian hierarchical framework, extending classical PCR in a variety of ways: modeling the latent principal components probabilistically to account for measurement error in the observational data, accommodating outliers that occur in the proxy data, and applying alternatives to the truncation of lower order principal components using regularization. One fundamental challenge in paleoclimate reconstruction efforts is the lack of out-of-sample data for predictive validation. Cross-validation is of potential value, but is computationally expensive and potentially sensitive to outliers in sparse data scenarios. We test our methods using a simulation study, applying proper scoring rules including a computationally efficient approximation to leave-one-out cross-validation using the log score to validate model performance.