LASPATED: A Library for the Analysis of Spatio-Temporal Discrete Data

In many settings, a user would like to use data of events that occur at points in space and time to estimate the intensity or rate of these events as a function of space and time. A nonhomogeneous Poisson process is a stochastic point process over space and/or time that is entirely specified by its intensity function, and is therefore a simple and popular stochastic model of random events in space and time.

We describe methods, tools, and a software library called LASPATED to fit nonhomogeneous spatio-temporal Poisson process models using spatio-temporal data and space-time discretization. The methods construct an intensity function for the Poisson process by discretizing space and time, and estimating arrival intensity as a function of subregion and time interval. With such methods, it is typical that the dimension of the estimator is large relative to the amount of data, and therefore the software makes provision for the use of additional data. The first method considered uses additional data to add a regularization term to the likelihood function for estimating the intensity of the Poisson process. The second method considered uses additional data to estimate arrival intensity as a function of covariates. We describe how the LASPATED Python and C++ packages perform various types of space and time discretization, and how they calibrate Poisson models, with options to use regularization or covariates. We demonstrate the use of the methods with simulated and real data. LASPATED can be used to estimate nonhomogeneous spatio-temporal Poisson process models for a wide range of applications, such as crime rates, earthquake rates, weather events, medical events, and fires.