Accessing difficult to reach hydrocarbon reservoirs while simultaneously reducing risk and increasing efficiency demonstrates a need for improved autonomous directional control of rotary steerable systems (RSS). The inherently uncertain drilling environment presents a challenge for control algorithms and human operators alike, where model mismatch can be significant and the parameters are time varying. Parameter estimation can improve the performance of steering controllers through model adaptation as well as provide valuable information to human operators. This paper proposes the use of a Markov Chain Monte Carlo (MCMC) method to estimate time-varying model parameters in real-time using only measurements commonly obtained while drilling. The proposed method is evaluated on historical field data and its accuracy is quantified by prediction accuracy to achieve a mean absolute error of 0.68 deg over 30 m. Next, the proposed method is used to adapt the model of a model predictive controller (MPC) and its performance is compared with a static MPC in closed-loop simulation of a prototypical drilling scenario. The estimator reduces tracking error of the MPC by 93.36% and produces a higher quality borehole. Finally, the utility of estimation for human-in-the-loop operation is explored through the design of an early warning system (EWS). The posterior distribution produced by MCMC is utilized in the EWS to predict the probability of undesirable future trajectories. By providing automatic alerts, the EWS serves as a safety mechanism that enhances operators' proficiency when monitoring several autonomously drilled wells.