This thesis proposes the use of a probabilistic state-space model with mixed-linear dynamics for learning to predict a robot's experiences. It is motivated by a desire to bridge the gap between traditional models with predefined objective semantics on the one hand, and the biologically-inspired "black box" behavioural paradigm on the other. A novel EM-type algorithm for the model is presented, which is less compuationally demanding than the Monte Carlo techniques developed for use in (for example) visual applications. The algorithm's E-step is slightly approximative, but an extension is described which would in principle make it asymptotically correct. Investigation using synthetically sampled data shows that the uncorrected E-step can any case make correct inferences about quite complicated systems. Results collected from two simulated mobile robot environments support the claim that mixed-linear models can capture both discontinuous and continuous structure in world in an intuitively natural manner; while they proved to perform only slightly better than simpler autoregressive hidden Markov models on these simple tasks, it is possible to claim tentatively that they might scale more effectively to environments in which trends over time played a larger role. Bayesian confidence regions—easily by mixed-linear model— proved be an effective guard for preventing it from making over-confident predictions outside its area of competence. A section on future extensions discusses how the model's easy invertibility could be harnessed to the ultimate aim of choosing actions, from a continuous space of possibilities, which maximise the robot's expected payoff over several steps into the future