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Gaussian processes are the workhorse for statistical modeling of space-time environmental processes, either directly or as a building block in various non-Gaussian process models. Unfortunately, exact evaluation of a Gaussian likelihood for as few as 10,000 irregular sited observations from such a process can be difficult to calculate on a desktop computer because of constraints on memory and/or floating point operations. In an informal chalk talk, I will discuss various approaches that have been suggested for dealing with this problem, including stochastic approximations, covariance tapering and composite likelhoods. I will argue that the best general approach is what I would call one-sided composite likelihoods (or the Vecchia approach) and try to explain why and when this approach should work well.
This talk represents joint work with Mihai Anitescu, Jie Chen, Michael
Horrell and Ying Sun.