Homogeneity and identity tests for unidimensional Poisson processes with an application to neurophysiological peri-stimulus time histograms

Christophe Pouzat (1) , Antoine Chaffiol (2) , Avner Bar-Hen (1)

1 MAP5 - UMR 8145 - Mathématiques Appliquées Paris 5
2 PISC - Physiologie de l'Insecte : Signalisation et Communication

The first characterization of the response of a neuron to a stimulus is the peri-stimulus time histogram (PSTH). From a statistical viewpoint the PSTH is an estimator of the intensity of the inhomogeneous Pois-son process describing (asymptotically) the aggregated responses of the neuron to repeated presentations of the stimulus. The PSTH is often used to address qualitatively two questions: i) is the neuron responding to the stimulation? ii) are the responses of a neuron to two different stimuli different? We propose here quantitative answers based of the PSTH. The observed state space is first finely binned before applying a variance stabilizing transformation. The homogeneity ("Is the neuron responding?") 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 ("Are the two responses identical?") 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 publicly avail-able. Our proposed methods are implemented in publicly available and documented codes for either R or Python.

Mots clés: Donsker Theorem; Brownian motion; Variance stabilization; Gaussian process; Kernel Estimation; Reproducible research

Domaines: Neurobiologie; Applications [stat.AP]

Christophe Pouzat, Antoine Chaffiol, Avner Bar-Hen. Homogeneity and identity tests for unidimensional Poisson processes with an application to neurophysiological peri-stimulus time histograms. 2015. ⟨hal-01113126v2⟩