Multivariate bias adjusted tapered predictive process models

We extend prior work on multivariate “low-rank” methods for the analysis of large multivariate spatial datasets. “Low-rank” methods usually operate on lower-dimensional subspaces and induce biases in the residual variance component as a result of over-smoothing or model mis-specification. Our current work attempts to characterize these biases, demonstrates their presence as a systemic phenomena, and explores remedial models without incurring computational costs. Our methodological contribution lies in the development of the multivariate tapered predictive process model that accounts for spatial correlations among multivariate components by the recently proposed multivariate matern correlation kernel. Both the proposed framework and the multivariate tapered predictive process model using linear model co-regionalization (LMC) (Sang et al., 2011) have been found to rectify bias in parameter estimation. We also prove novel theoretical results comparing smoothness properties of multivariate tapered predictive process models and classes of low rank models, including predictive processes. Finally, we illustrate our work using synthetic experiments as well as an application to forestry.