Retinal microsurgery is a high-precision surgery performed on an exceedingly delicate tissue. It now requires extensively trained and highly skilled surgeons. Given the restricted range of instrument motion in the confined intraocular space, and also potentially restricting instrument contact with the sclera, snake-like robots may prove to be a promising technology to provide surgeons with greater flexibility, dexterity, space access, and positioning accuracy during retinal procedures requiring high precision and advantageous tooltip approach angles, such as retinal vein cannulation and epiretinal membrane peeling. Kinematics modeling of these robots is an essential step toward accurate position control, however, as opposed to conventional manipulators, modeling of these robots does not follow a straightforward method due to their complex mechanical structure and actuation mechanisms. Especially, in wire-driven snake-like robots, the hysteresis problem due to the wire tension condition can have a significant impact on the positioning accuracy of these robots. In this paper, we proposed an experimental kinematics model with a hysteresis compensation algorithm using the probabilistic Gaussian mixture models (GMM) Gaussian mixture regression (GMR) approach. Experimental results on the two-degree-of-freedom (DOF) integrated robotic intraocular snake (I2RIS) show that the proposed model provides 0.4 deg accuracy, which is an overall 60% and 70% of improvement for yaw and pitch degrees of freedom, respectively, compared to a previous model of this robot.