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The robust detection of statistical dependencies between the components of acomplex system is a key step in gaining a network-based understanding of thesystem. Because of their simplicity and low computation cost, pairwisestatistics are commonly used in a variety of fields. Those approaches, however,typically suffer from one or more limitations such as lack of confidenceintervals requiring reliance on surrogate data, sensitivity to binning,sparsity of the signals, or short duration of the records. In this paper wedevelop a method for assessing pairwise dependencies in point processes thatovercomes these challenges. Given two point processes $X$ and $Y$ each emittinga given number of events $m$ and $n$ in a fixed period of time $T$, we deriveexact analytical expressions for the expected value and standard deviation ofthe number of pairs events $X_i,Y_j$ separated by a delay of less than $\tau$one should expect to observe if $X$ and $Y$ were i.i.d. uniform randomvariables. We prove that this statistic is normally distributed in the limit oflarge $T$, which enables the definition of a Z-score characterising thelikelihood of the observed number of coincident events happening by chance. Wenumerically confirm the analytical results and show that the property ofnormality is robust in a wide range of experimental conditions. We thenexperimentally demonstrate the predictive power of the method using a noisyversion of the common shock model. Our results show that our approach hasexcellent behaviour even in scenarios with low event density and/or when therecordings are short.

A new method for the robust characterisation of pairwise statistical dependency between point processes