In this paper, a new calibration method for open-chain robotic arms is developed. By incorporating both prior parameter information and artifact measurement data, and by taking recourse to Bayesian inference methods, not only are the robot kinematic parameters updated but also confidence bounds are computed for all measurement data. In other words, for future measurement data not only the most likely end-effector configuration is estimated but also the uncertainty represented as 95% confidence bounds of that pose is computed. To validate the proposed calibration method, a three degree-of-freedom robotic arm was designed, constructed, and calibrated using both typical regression methods and the proposed calibration method. The results of an extensive set of experiments are presented to gauge the accuracy and utility of the proposed calibration method.