  Mixture models have been around for over 150 years, as an intuitively simple
and practical tool for enriching the collection of probability distributions
available for modelling data. In this chapter we describe the basic ideas of
the subject, present several alternative representations and perspectives on
these models, and discuss some of the elements of inference about the unknowns
in the models. Our focus is on the simplest set-up, of finite mixture models,
but we discuss also how various simplifying assumptions can be relaxed to
generate the rich landscape of modelling and inference ideas traversed in the
rest of this book.
