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Large spatial datasets often represent a number of spatial point processesgenerated by distinct entities or classes of events. When crossed withcovariates, such as discrete time buckets, this can quickly result in a dataset with millions of individual density estimates. Applications that requiresimultaneous access to a substantial subset of these estimates become resourceconstrained when densities are stored in complex and incompatible formats. Wepresent a method for representing spatial densities along the nodes of sparselypopulated trees. Fast algorithms are provided for performing set operations andqueries on the resulting compact tree structures. The speed and simplicity ofthe approach is demonstrated on both real and simulated spatial data.

Sparse Density Representations for Simultaneous Inference on Large Spatial Datasets