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Spatial prediction requires expensive computation to invert the spatialcovariance matrix it depends on and also has considerable storage needs. Thiswork concentrates on computationally efficient algorithms for prediction usingvery large datasets. A recent prediction model for spatial data known as FixedRank Kriging is much faster than the kriging and can be easily implemented withless assumptions about the process. However, Fixed Rank Kriging requires theestimation of a matrix which must be positive definite and the originalestimation procedure cannot guarantee this property. We present a result thatshows when a matrix subtraction of a given form will give a positive definitematrix. Motivated by this result, we present an iterative Fixed Rank Krigingalgorithm that ensures positive definiteness of the matrix required forprediction and show that under mild conditions the algorithm numericallyconverges. The modified Fixed Rank Kriging procedure is implemented to predictmissing chlorophyll observations for very large regions of ocean color.Predictions are compared to those made by other well known methods of spatialprediction.

A Low Rank Gaussian Process Prediction Model for Very Large Datasets