In recent years Bayesian methods have become widespread in many domains such as computer vision, signal processing, information retrieval and genome data analysis. The availability of fast computers allows the required computations to be performed in reasonable time, and thereby makes the benefits of a Bayesian treatment accessible to an ever broadening range of applications. In this tutorial we give an overview of the Bayesian approach to pattern recognition in the context of simple regression and classification problems. We then describe in detail a specific Bayesian model for regression and classification called the `Relevance Vector Machine’. This overcomes many of the limitations of the widely used Support Vector Machines, whilst retaining the highly desirable property of sparseness.