This thesis discusses the use of Bayesian Inference in inferring over the human's objective for Human-Robot Interaction, more specifically, it focuses upon the adaptation of methods to better utilize the information for inferring upon the human's objective for Reward Learning and Communicative Shared Autonomy settings. To accomplish this, we first examine state-of-the-art methods for approaching Bayesian Inverse Reinforcement learning where we explore the strengths and weaknesses of current approaches. After which we explore alternative methods for approaching the problem, borrowing similar approaches to those of the statistics community to apply alternative methods to improve the sampling process over the human's belief. After this, I then move to a discussion on the setting of Shared Autonomy in the presence and absence of communication. These differences are then explored in our method for inferring upon an environment where the human is aware of the robot's intention and how this can be used to dramatically improve the robot's ability to cooperate and infer upon the human's objective. In total, I conclude that the use of these methods to better infer upon the human's objective significantly improves the performance and cohesion between the human and robot agents within these settings. / Master of Science / This thesis discusses the use of various methods to allow robots to better understand human actions so that they can learn and work with those humans. In this work we focus upon two areas of inferring the human's objective: The first is where we work with learning what things the human prioritizes when completing certain tasks to better utilize the information inherent in the environment to best learn those priorities such that a robot can replicate the given task. The second body of work surrounds Shared Autonomy where we work to have the robot better infer what task a human is going to do and thus better allow the robot to assist with this goal through using communicative interfaces to alter the information dynamic the robot uses to infer upon that human intent. Collectively, the work of the thesis works to push that the current inference methods for Human-Robot Interaction can be improved through the further progression of inference to best approximate the human's internal model in a given setting.