Multiple Tests Based on a Gaussian Approximation of the Unitary Events Method with Delayed Coincidence Count

Abstract

The unitary events (UE) method is one of the most popular and efficient methods used over the past decade to detect patterns of coincident joint spike activity among simultaneously recorded neurons. The detection of coincidences is usually based on binned coincidence count (Grün, 1996 ), which is known to be subject to loss in synchrony detection (Grün, Diesmann, Grammont, Riehle, & Aertsen, 1999 ). This defect has been corrected by the multiple shift coincidence count (Grün et al., 1999 ). The statistical properties of this count have not been further investigated until this work, the formula being more difficult to deal with than the original binned count. First, we propose a new notion of coincidence count, the delayed coincidence count, which is equal to the multiple shift coincidence count when discretized point processes are involved as models for the spike trains. Moreover, it generalizes this notion to nondiscretized point processes, allowing us to propose a new gaussian approximation of the count. Since unknown parameters are involved in the approximation, we perform a plug-in step, where unknown parameters are replaced by estimated ones, leading to a modification of the approximating distribution. Finally the method takes the multiplicity of the tests into account via a Benjamini and Hochberg approach (Benjamini & Hochberg, 1995 ), to guarantee a prescribed control of the false discovery rate. We compare our new method, MTGAUE (multiple tests based on a gaussian approximation of the unitary events) and the UE method proposed in Grün et al. ( 1999 ) over various simulations, showing that MTGAUE extends the validity of the previous method. In particular, MTGAUE is able to detect both profusion and lack of coincidences with respect to the independence case and is robust to changes in the underlying model. Furthermore MTGAUE is applied on real data.

Detection of dependence patterns with delay

“…Informally, there is a coincidence between neurons when they each emit a spike more or less simultaneously. This notion has already been used in UE methods (Grün et al., ) and is based on the following idea: a real dependency between neurons should be characterized by an unusually large (or low) number of coincidence (Grün, ; Grammont and Riehle, ; Tuleau‐Malot et al., ).…”

“…For more precise informations on the binning procedure and the link with point processes we refer the interested reader to Tuleau‐Malot et al. ().…”

“…However, following the study of Tuleau‐Malot et al. (), we have decided to focus on symmetric tests. Hence, the symmetric test based on the UE method rejects the independence hypothesis when is too different from .…”

“…First, let us present and discuss our main assumptions that are the same as in Tuleau‐Malot et al. (). Assumption are Poisson processes.…”

“…(), both of the improvements (Multiple Shift and MTGAUE) can only consider pairs of neurons. Thus, our goal is to generalize the method introduced in (Tuleau‐Malot et al., ) for more than two neurons. Unlike MTGAUE, our test is not designed to be performed on multiple time windows.…”