Spatial Design for Knot Selection in Knot-Based Dimension Reduction Models
This chapter addresses the settings where there is need to specify knots in order to fit desired spatial models. That is, it seeks to fit hierarchical models in order to enable full inference and to adequately capture uncertainty. The chapter adopts an approximate model to make computation feasible. It provides a brief review of different approaches to modeling large point-referenced datasets. The chapter focuses on knot-based dimension reduction using low rank models/approximations and the predictive process in particular. It discusses some basic ideas for designing knots and connects this objective with existing knowledge on spatial designs. A specific strategy for knot-design for predictive process models outlined presents some numerical examples using simulated data as well as a forestry dataset and the Austria monitoring network dataset.
