Surrogate Data Methods Based on a Shuffling of the Trials for Synchrony Detection: The Centering Issue

Abstract

We investigate several distribution-free dependence detection procedures, all based on a shuffling of the trials, from a statistical point of view. The mathematical justification of such procedures lies in the bootstrap principle and its approximation properties. In particular, we show that such a shuffling has mainly to be done on centered quantities-that is, quantities with zero mean under independence-to construct correct p-values, meaning that the corresponding tests control their false positive (FP) rate. Thanks to this study, we introduce a method, named permutation UE, which consists of a multiple testing procedure based on permutation of experimental trials and delayed coincidence count. Each involved single test of this procedure achieves the prescribed level, so that the corresponding multiple testing procedure controls the false discovery rate (FDR), and this with as few assumptions as possible on the underneath distribution, except independence and identical distribution across trials. The mathematical meaning of this assumption is discussed, and it is in particular argued that it does not mean what is commonly referred in neuroscience to as cross-trials stationarity. Some simulations show, moreover, that permutation UE outperforms the trial-shuffling of Pipa and Grün ( 2003 ) and the MTGAUE method of Tuleau-Malot et al. ( 2014 ) in terms of single levels and FDR, for a comparable amount of false negatives. Application to real data is also provided.

Concentration Inequalities for Randomly Permuted Sums

“…Yet, as explained above, such purely asymptotic properties may be insufficient when applying these tests in neuroscience for instance. Moreover, the delicate choice of the parameter δ is a real question, especially, in neuroscience, where it has some biological meaning, as mentioned in [ABFRB15] and [ABFRB16]. A possible approach to overcome this issue is to aggregate several tests for different parameters δ, and reject independence if at least one of them does.…”

Computational Neuroscience: Mathematical and Statistical Perspectives

“…While this illustrated the potential role of precisely timed spikes, it also raised the issue of whether other plausible point process null models might lead to different results. Much work has been done to refine this methodology (Albert et al 2016; Gmn 2009; Torre et al 2016). Related approaches replace the null assumption of independence with some order of correlation, using marked Poisson processes (Staude et al 2010).…”

Thermodynamic Formalism in Neuronal Dynamics and Spike Train Statistics

“…This gave rise to major branches of theoretical neuroscience, like dynamic mean-field methods [29,[152][153][154] or the Maximum Entropy approach [38,49,148,155], mainly coming from physicists. Although there are considerably less articles using mathematical methods to rigorously analyse the collective behaviour of neuronal networks some promising approach have been recently proposed based on large deviations [156,157], Kalikow-type decomposition [91,158], stochastic processes [159][160][161][162][163], dynamical systems [137,164], etc. As we have developed in this review, Thermodynamic Formalism could also be one of these tools, providing interesting connections between mathematics and physics, dynamics and statistics, applied to neuroscience.…”