Table 2.

Table of methods and stochastic models

Method	Pairwise correlation	Synchronous patterns	Population synchronization	STPs	SSEs
Complexity distribution	$(✓)$	$(✓)$	$✓$		$(✓)$
CuBIC	$(✓)$	$(✓)$	$✓$		$(✓)$
PUE	$(✓)$	$(✓)$	$✓$		$(✓)$
Max. entropy information	$✓$		${✓}^{\ast }$
Max. entropy models	$✓$	${✓}^{\ast }$
Cliques	$✓$	$(✓)$	$(✓)$		$(✓)$
SPADE	$(✓)$	$✓$	$(✓)$	$✓$	$✓$
CAD	$(✓)$	$✓$	$(✓)$	$✓$	$✓$
ASSET					$✓$

The table summarizes the ability of each method to retrieve correlations represented by different models. $✓$: the method is designed to detect that particular model and the output matches perfectly and describes completely the correlation structure of the data. $(✓):$ The method was designed for a different correlation model, but it is still possible to get partial information about the correlation structure of the data. ${✓}^{\ast }$: The method is in principle applicable, but in practice affected by computational and/or multiple testing issues when used on MPST data; the results may lead to misinterpret the correlation structure due to lack of information about it. For the remaining entries, the method does not provide sufficient information to reconstruct the correlation structure