To facilitate interaction with people, robots must not only recognize current actions, but also infer a person's intentions and future behavior. Recent advances in depth camera technology have significantly improved human motion tracking. However, the inherent high dimensionality of interacting with the physical world makes efficiently forecasting human intention and future behavior a challenging task. Predictive methods that estimate uncertainty are therefore critical for supporting appropriate robotic responses to the many ambiguities posed within the human-robot interaction setting. We address these two challenges, high dimensionality and uncertainty, by employing predictive inverse optimal control methods to estimate a probabilistic model of human motion trajectories. Our inverse optimal control formulation estimates quadratic cost functions that best rationalize observed trajectories framed as solutions to linear-quadratic regularization problems. The formulation calibrates its uncertainty from observed motion trajectories, and is efficient in high-dimensional state spaces with linear dynamics. We demonstrate its effectiveness on a task of anticipating the future trajectories, target locations and activity intentions of hand motions.