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A model of Poissonian interactions and detection of dependence

Laure Sansonnet,Christine Tuleau-Malot

Published 2013 in Statistics and computing

ABSTRACT

This paper proposes a model of interactions between two point processes, ruled by a reproduction function h, which is considered as the intensity of a Poisson process. In particular, we focus on the context of neuroscience to detect possible interactions in the cerebral activity associated with two neurons. To provide a mathematical answer to this specific problem of neurobiologists, we address so the question of testing the nullity of the intensity h. We construct a multiple testing procedure obtained by the aggregation of single tests based on a wavelet thresholding method. This test has good theoretical properties: it is possible to guarantee the level but also the power under some assumptions and its uniform separation rate over weak Besov bodies is adaptive minimax. Then, some simulations are provided, showing the good practical behavior and the robustness of our testing procedure.

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