We develop a Bayesian sequential model for category learning. The sequential model updates two category parameters, the mean and the variance, over time. We define conjugate temporal priors to enable closed form solutions to be obtained. This model can be easily extended to supervised and unsupervised learning involving multiple categories. To model the spacing effect, we introduce a generic prior in the temporal updating stage to capture a learning preference, namely, less change for repetition and more change for variation. Finally, we show how this approach can be generalized to efficiently perform model selection to decide whether observations are from one or multiple categories. 1

Normative theories of learning and decision-making are motivated by a computational-level analysis of the task facing an animal: what should the animal do to maximize future reward? However, much of the recent excitement in this field originates in how the animal arrives at its decisions and reward predictions—-algorithmic questions about which the computational-level analysis is silent.

Statistical decision theory seems to offer a clear framework for the integration of perception and action. In particular, it defines the problem of maximizing the utility of one’s decisions in terms of two subtasks: inferring the likely state of the world, and tracking the utility that would result from different candidate actions in different states. This computational-level description underpins more processlevel research in neuroscience about the brain’s dynamic mechanisms for, on the one hand, inferring states and, on the other hand, learning action values. However, a number of different strands of recent work on this more algorithmic level have cast doubt on the basic shape of the decision-theoretic formulation, specifically the clean separation between states ’ probabilities and utilities. We consider the complex interrelationship between perception, action, and utility implied by these accounts. Normative theories of learning and decision making are motivated by a computational-level analysis of the task facing an organism: What should