Examples of joint probability density distributions, used for computation of mutual information (MI). The distributions were estimated by applying a Gaussian kernel to: A. Eye position samples between 5 and 10 ms from saccade initiation; B. Eye velocity samples between 5 and 10 ms; C. Eye position samples between 90 and 100 ms; D. Eye velocity samples between 90 and 100 ms. The smoothing length of the kernel was optimized based on the samples by the likelihood cross validation method. The distributions are for a leftward saccade, Go/NoGo session on the 1st day. Left panel: The samples were paired between the eyes in each trial with no delay. The MI of the original paired samples (MIOri) and its correlation coefficient (CROri) are noted on the top left of each panel. Right panel: The pairs were randomized among trials within the time window of 11 ms. Because of the finite sample size (330 pairs). the MI of randomized samples (MIRan) was often significantly larger than zero in spite of the randomization procedure. The MIRan was used to estimate the overestimation of relationship. The CROri did not overestimate the relationship as shown by the correlation coefficient of the randomized samples (CRRan). The probability densities are indicated by the colors, as specified in the color scales. The units of velocity are (deg/s)-2 and position deg-2.