Definition Gaussian processes (GPs) are local approximation techniques that model spatial data by placing (and updating) priors on the covariance structures underlying the data. Originally developed for geo-spatial contexts, they are also applicable in general contexts that involve computing and modeling with multi-level spatial aggregates, e.g., modeling a configuration space for crystallographic design, casting folding energies as a function of a protein's contact map, and formulation of

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... nation policies taking into account social dynamics of individuals. Typically, we assume a parametrized covariance structure underlying the data to be modeled. We estimate the covariance parameters conditional on the locations for which we have observed data, and use the inferred structure to make predictions at new locations. GPs have a probabilistic basis that allow us to estimate variances at unsampled locations, aiding in the design of targeted sampling strategies. Historical Background The underlying ideas behind GPs can be traced back to the geostatistics technique called kriging (Journel and Huijbregts 1992), named after the South African miner Danie Krige. Kriging in this literature was used to model response variables (e.g., ozone concentrations) over 2D spatial fields as realizations of a stochastic process. Sacks et al. (1989) described the use of kriging to model (deterministic) computer experiments. It took more than a decade from this point for the larger computer science community to investigate GPs for pattern analysis purposes. Thus, in the recent past, GPs have witnessed a revival primarily due to work in