Estimating mutual information and Pearson correlation on neural evoked responses

In neural evoked responses, small variations in the timing or duration of responses can be observed when the same functional response is recorded in different trials, different experimental conditions or by different sensors. These variations limit the ability of correlation-based methods to detect similarities between signals. Mutual information (MI) provides an alternative similarity measure, capable of capturing both linear and non-linear dependencies, yet its practical use is hindered by lack of consensus on estimators for continuous data and the limited understanding of the behavior of the estimators on realistic signals. In this work, we investigate how to estimate the similarity of neural evoked responses by systematically comparing sample Pearson correlation with three of the most common MI estimators. We describe their behavior using both simulated signals and real magnetoencephalographic data. In the simulations, the estimators are tested against a set of transformations that depict realistic changes in neural evoked responses. Subsequently, we propose guidelines for defining adaptive lower bounds on the similarity estimates and analyzing the similarity rankings induced by the different estimators. Our findings reveal trade-offs between measures sensitivity and different signal properties. We confirm that Pearson correlation is reliable in describing linear relationships for low-noise signals, and we identify parameter settings that stabilize MI estimators, enabling them to capture complex signal dependencies. Together, these results introduce practical parameter choices and thresholding strategies for mutual information and provide guidance for selecting and interpreting similarity measures in the analysis of neural evoked time series.