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spatialAtRisk(X, ...)
Generic function used in the construction of spatialAtRisk objects. The class of spatialAtRisk objects provide a framework for describing the spatial inhomogeneity of the at-risk population, lambda(s). This is in contrast to the class of temporalAtRisk objects, which describe the global levels of the population at risk, mu(t).
Unless the user has specified lambda(s) directly by an R function (a mapping the from the real plane onto the non-negative real numbers, see ?spatialAtRisk.function), then it is only necessary to describe the population at risk up to a constant of proportionality, as the routines automatically normalise the lambda provided to integrate to 1.
For reference purposes, the following is a mathematical description of a log-Gaussian Cox Process, it is best viewed in the pdf version of the manual.
Let $\mathcal Y(s,t)$ be a spatiotemporal Gaussian process, $W\subset R^2$ be an
observation window in space and $T\subset R_{\geq 0}$ be an interval of time of interest.
Cases occur at spatio-temporal positions $(x,t) \in W \times T$
according to an inhomogeneous spatio-temporal Cox process,
i.e. a Poisson process with a stochastic intensity $R(x,t)$,
The number of cases, $X_{S,[t_1,t_2]}$, arising in
any $S \subseteq W$ during the interval $[t_1,t_2]\subseteq T$ is
then Poisson distributed conditional on $R(\cdot)$,