ABSTRACT
Coupling processes together, for example to warp a nonstationary surface into one wherein simpler stationary dynamics reign adds layers of additional computational complexity and/or requires Markov chain Monte Carlo. This chapter focuses on Gaussian process (GP) methods which address those two issues, computational thrift and modeling fidelity, simultaneously. GPs can only be brought to bear on modern big data problems in statistics and machine learning by somehow skirting full dense matrix decomposition. The literature on nonstationary modeling is more niche, although growing. Only a couple of the ideas offer promise in the face of both computational and modeling challenges. The chapter illustrates a distance-based kernel which guarantees both sparsity and positive definiteness, however as a device that technique underwhelms. Sparse kernels compromise on long-range structure without gaining enhanced local modeling fidelity.
