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A model of Poissonian interactions and detection of dependence

Abstract : Abstract:This paper proposes a model of interactions between two point pro-cesses, ruled by a reproduction functionh, which is considered as the intensity ofa Poisson process. In particular, we focus on the context of neuroscience to detectpossible interactions in the cerebral activity associatedwith two neurons. To pro-vide a mathematical answer to this specific problem of neurobiologists, we addressso the question of testing the nullity of the intensityh. We construct a multipletesting procedure obtained by the aggregation of single tests based on a waveletthresholding method. This test has good theoretical properties: it is possible toguarantee the level but also the power under some assumptions and its uniform sep-aration 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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https://hal-agroparistech.archives-ouvertes.fr/hal-01568807
Contributor : Armelle Sielinou <>
Submitted on : Tuesday, July 25, 2017 - 5:51:29 PM
Last modification on : Friday, February 5, 2021 - 3:50:12 AM

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  • HAL Id : hal-01568807, version 1

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Laure Sansonnet, Christine Tuleau-Malot. A model of Poissonian interactions and detection of dependence. Statistics and Computing, Springer Verlag (Germany), 2015, 25 (2), pp.449-470. ⟨hal-01568807⟩

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