# Introduction to finite mixtures

## TL;DR

This chapter introduces finite mixture models, explaining their basic concepts, representations, and inference methods, while discussing extensions and simplifications for practical data modeling.

## Contribution

It provides a comprehensive overview of finite mixture models, including their representations, inference techniques, and ways to relax assumptions for broader applicability.

## Key findings

- Finite mixture models are versatile for data modeling.
- Various representations facilitate understanding and inference.
- Extensions allow relaxing simplifying assumptions.

## Abstract

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.