A model of Poissonian interactions and detection of dependence
| Autor: | Christine Tuleau-Malot, Laure Sansonnet |
|---|---|
| Přispěvatelé: | Mathématiques et Informatique Appliquées (MIA-Paris), AgroParisTech-Institut National de la Recherche Agronomique (INRA), Laboratoire de Mathématiques d'Orsay (LM-Orsay), Centre National de la Recherche Scientifique (CNRS)-Université Paris-Sud - Paris 11 (UP11), Laboratoire Jean Alexandre Dieudonné (JAD), Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS), French Agence Nationale de la Recherche ANR 2011 BS01 010 01, COMUE Université Côte d'Azur (2015 - 2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015 - 2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS) |
| Rok vydání: | 2013 |
| Předmět: |
Statistics and Probability
uni-form separation rate [SDV]Life Sciences [q-bio] uniform separation rate Mathematics - Statistics Theory Context (language use) Poisson process Statistics Theory (math.ST) wavelets Point process interactions model Theoretical Computer Science neuroscience symbols.namesake weak Besovbodies [MATH.MATH-ST]Mathematics [math]/Statistics [math.ST] FOS: Mathematics Statistical physics weak Besov bodies 62G10 62G20 62G30 ComputingMilieux_MISCELLANEOUS Mathematics neurosciences [STAT.TH]Statistics [stat]/Statistics Theory [stat.TH] Minimax Unitary Events Power (physics) Computational Theory and Mathematics Adaptive tests Multiple comparisons problem symbols Statistics Probability and Uncertainty Focus (optics) Intensity (heat transfer) |
| Zdroj: | Statistics and Computing Statistics and Computing, Springer Verlag (Germany), 2015, 25 (2), pp.449-470 Statistics and Computing, Springer Verlag (Germany), 2013, 25 (2), pp.10.1007/s11222-013-9443-z. ⟨10.1007/s11222-013-9443-z⟩ |
| ISSN: | 0960-3174 1573-1375 |
| DOI: | 10.48550/arxiv.1301.5802 |
| Popis: | 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 neurosciences 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 of our testing procedure. Comment: 27 pages |
| Databáze: | OpenAIRE |
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