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Modeling spatial overdispersion requires point processes models with finitedimensional distributions that are overdisperse relative to the Poisson.Fitting such models usually heavily relies on the properties of stationarity,ergodicity, and orderliness. And, though processes based on negative binomialfinite dimensional distributions have been widely considered, they typicallyfail to simultaneously satisfy the three required properties for fitting.Indeed, it has been conjectured by Diggle and Milne that no negative binomialmodel can satisfy all three properties. In light of this, we changeperspective, and construct a new process based on a different overdispersecount model, the Generalized Waring Distribution. While comparably tractableand flexible to negative binomial processes, the Generalized Waring process isshown to possess all required properties, and additionally span the negativebinomial and Poisson processes as limiting cases. In this sense, the GW processprovides an approximate resolution to the conundrum highlighted by Diggle andMilne.

Modeling Spatial Overdispersion with the Generalized Waring Process