Decision making and planning with partial state information is a problem faced by all forms of intelligent entities. The formulation of a problem under partial state information leads to an exorbitant set of choices with associated probabilistic outcomes making its resolution difficult when using traditional planning methods. Human beings have acquired the ability of acting under uncertainty through education and self-learning. Transferring our know-how to artificial agents and robots will make it faster for them to learn and even improve upon us in tasks in which incomplete knowledge is available, which is the objective of this thesis. We model how humans reason with respect to their beliefs and transfer this knowledge in the form of a parameterised policy, following a Programming by Demonstration framework, to a robot apprentice for two spatial navigation tasks: the first task consists of localising a wooden block on a table and for the second task a power socket must be found and connected. In both tasks the human teacher and robot apprentice only rely on haptic and tactile information. We model the human and robot's beliefs by a probability density function which we update through recursive Bayesian state space estimation. To model the reasoning processes of human subjects performing the search tasks we learn a generative joint distribution over beliefs and actions (end-effector velocities) which were recorded during the executions of the task. For the first search task the direct mapping from belief to actions is learned whilst for the second task we incorporate a cost function used to adapt the policy parameters in a Reinforcement Learning framework and show a considerable improvement over solely learning the behaviour with respect to the distance taken to accomplish the task. Both search tasks above can be considered as active localisation as the uncertainty originates only from the position of the agent in the world. We consider searches in which both the position of the robot and features of the environment are uncertain. Given the unstructured nature of the belief a histogram parametrisation of the joint distribution of the robots position and features is necessary. However, naively doing so becomes quickly intractable as the space and time complexity is exponential. We demonstrate that by only parametrising the marginals and by memorising the parameters of the measurement likelihood functions we can recover the exact same solution as the naive parametrisations at a cost which is linear in space and time complexity.