Homogeneity and identity tests for Poisson processes: Application to neuronal Peri-Stimulus Time Histograms (PSTHs)

Speaker: Christophe Pouzat / Paris-Descartes University
Date: Apr 16, 2015
Time: 14h00
Local: Numec´s multipurpose room

strong>Abstract: This presentation will focus on two classical questions met in neurophysiology when studying the response to a given stimulus: i) is the neuron responding to the stimulation? ii) are the responses of a neuron to two different stimuli different? To achieve these aims we study the statistical properties of the peri-stimulus time histogram (PSTH), an estimator of the intensity of the Poisson process describing the aggregation of the successive responses. In a nutshell, we propose to finely bin the observed state space before applying a variance stabilizing transformation. The homogeneity is then addressed by using a linear smoother estimator for the scaled Poisson process intensity before building a confidence set containing this estimator. The identity is addressed by constructing the cumulative sum of the difference of the scaled PSTH obtained with the two stimuli. This cumulative sum tends under the null hypothesis towards a canonical Brownian motion. Minimal surface domains containing the totality of a given fraction of the realizations of a canonical Brownian motion are available, allowing us to build an identity test. Our motivating dataset arises from our own experimental work and is now publicly available on zenodo: after recording the spontaneous activity for a few minutes, a cockroach (Periplaneta americana) was stimulated with an odor: citronellal, terpineol or a 50/50 mixture of the two. The recordings were made from the first olfactory relay of the insect with an interval between stimulation long enough for the effect of the former to have disappeared when the next comes. This is a joint work with Antoine Chaffiol and Avner Bar-Hen.



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