Similar to the use of likelihood, we might instead first use the actual events to form a density surface, using some KDE method, and then comparing this risk surface against the predicted one.
This is suggested in [1], in a medical imaging context (cellular morphology). The proposed way to compare two kernels is via integrated square error $$ T = \int \big|f(x) - p(x)\big|^2 $$ where $f$ is the kernel estimated from the actual events, and $p$ is the prediction. When both $f$ and $p$ are estimated from a fixed bandwidth KDE, it is possible to expand out the integral defining $T$ and proceed at least partly analytically, which is how [1] proceeds. In our case, $p$ will often not be given by an explicit KDE method. Furthermore, we also wish to consider the "edge correction" methods as suggested by [2].
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