On Goodness of Fit Tests For Models of Neuronal Spike Trains Considered as Counting Processes

Details On Goodness of Fit Tests For Models of Neuronal Spike Trains Considered as Counting Processes On Goodness of Fit Tests For Models of Neuronal Spike Trains Considered as Counting Processes

2009-09-15

arxiv.org/abs/0909.2785v1

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After an elementary derivation of the "time transformation", mapping a counting process onto a homogeneous Poisson process with rate one, a brief review of Ogata's goodness of fit tests is presented and a new test, the "Wiener process test", is proposed. This test is based on a straightforward application of Donsker's Theorem to the intervals of time transformed counting processes. The finite sample properties of the test are studied by Monte Carlo simulations. Performances on simulated as well as on real data are presented. It is argued that due to its good finite sample properties, the new test is both a simple and a useful complement to Ogata's tests. Warnings are moreover given against the use of a single goodness of fit test.

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