he focus of this chapter will be on problems in higher-level cognition: inferring causal structure from patterns of statistical correlation, learning about categories and hidden properties of objects, and learning the meanings of words. This focus is partly a pragmatic choice, as these topics are the sub- ject of our own research and hence we know them best. But there are also deeper rea- sons for this choice. Learning about causal relations, category structures, or the proper- ties or names of objects are problems that are very close to the classic problems of induction that have been much discussed and puzzled over in the Western philo- sophical tradition. Showing how Bayesian methods can apply to these problems thus illustrates clearly their importance in un- derstanding phenomena of induction more generally. These are also cases where the im- portant mathematical principles and tech- niques of Bayesian statistics can be applied in a relatively straightforward way. They thus provide an ideal training ground for readers new to Bayesian modeling.