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A model of Poissonian interactions and detection of dependence. Arxiv
, 2013
"... Abstract: This paper proposes a model of interactions between two point pro-cesses, 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 associate ..."
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Abstract: This paper proposes a model of interactions between two point pro-cesses, 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 pro-vide 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 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.
BOOTSTRAP AND PERMUTATION TESTS OF INDEPENDENCE FOR POINT PROCESSES
, 2015
"... Motivated by a neuroscience question about synchrony detection in spike train analysis, we deal with the independence testing problem for point processes. We introduce nonparametric test statistics, which are rescaled general U-statistics, whose corresponding critical values are constructed from boo ..."
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Motivated by a neuroscience question about synchrony detection in spike train analysis, we deal with the independence testing problem for point processes. We introduce nonparametric test statistics, which are rescaled general U-statistics, whose corresponding critical values are constructed from bootstrap and randomization/permutation approaches, making as few assumptions as possible on the underlying distribution of the point processes. We derive general consistency results for the bootstrap and for the permutation w.r.t. Wasserstein’s metric, which induces weak convergence as well as convergence of second-order moments. The obtained bootstrap or permutation independence tests are thus proved to be asymptotically of the prescribed size, and to be consistent against any reasonable alternative. A simulation study is performed to illustrate the derived theoretical results, and to compare the performance of our new tests with existing ones in the neuroscientific literature.
and
, 2013
"... 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 neurosciences to detect possible interactions in the cerebral activity associate ..."
Abstract
- Add to MetaCart
(Show Context)
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 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.
