3 research outputs found
Detection of dependence patterns with delay
The Unitary Events (UE) method is a popular and efficient method used this
last decade to detect dependence patterns of joint spike activity among
simultaneously recorded neurons. The first introduced method is based on binned
coincidence count \citep{Grun1996} and can be applied on two or more
simultaneously recorded neurons. Among the improvements of the methods, a
transposition to the continuous framework has recently been proposed in
\citep{muino2014frequent} and fully investigated in \citep{MTGAUE} for two
neurons. The goal of the present paper is to extend this study to more than two
neurons. The main result is the determination of the limit distribution of the
coincidence count. This leads to the construction of an independence test
between neurons. Finally we propose a multiple test procedure via a
Benjamini and Hochberg approach \citep{Benjamini1995}. All the theoretical
results are illustrated by a simulation study, and compared to the UE method
proposed in \citep{Grun2002}. Furthermore our method is applied on real data
Analyzing dependence between point processes in time using IndTestPP
The need to analyze the dependence between two or more point processes in time appears in many modeling problems related to the occurrence of events, such as the occurrence of climate events at different spatial locations or synchrony detection in spike train analysis. The package IndTestPP provides a general framework for all the steps in this type of analysis, and one of its main features is the implementation of three families of tests to study independence given the intensities of the processes, which are not only useful to assess independence but also to identify factors causing dependence. The package also includes functions for generating different types of dependent point processes, and implements computational statistical inference tools using them. An application to characterize the dependence between the occurrence of extreme heat events in three Spanish locations using the package is shown
Fluctuations for mean-field interacting age-dependent Hawkes processes
The propagation of chaos and associated law of large numbers for mean-field
interacting age-dependent Hawkes processes (when the number of processes n goes
to +) being granted by the study performed in (Chevallier, 2015), the
aim of the present paper is to prove the resulting functional central limit
theorem. It involves the study of a measure-valued process describing the
fluctuations (at scale n --1/2) of the empirical measure of the ages around its
limit value. This fluctuation process is proved to converge towards a limit
process characterized by a limit system of stochastic differential equations
driven by a Gaussian noise instead of Poisson (which occurs for the law of
large numbers limit)