Unbiased estimation of the population-level motor module

Summary Motor module is a functional neurophysiological command for muscle coordination. In clinical settings, population-level characterization and comparison of motor modules are necessary to evaluate pathophysiological mechanisms and intervention effects. Previous studies have estimated individual motor modules and then compared them, but the validity of capturing the distribution of the latent population has not been fully understood. Our study aimed to address this issue by investigating the accuracy of estimating the population mean of motor modules. Through simulation experiments, we found that previous individual-based approach did not converge regardless of sample size and was vulnerable to noise. We developed an unbiased estimation algorithm using the framework of functional data analysis, which significantly improved estimation accuracy. Our findings highlight statistical challenges for motor module analysis and suggest the need for further research on new computational algorithms using large-scale clinical data. Graphical Abstract