- In this course we learn to:
📋 The Course in Context
This is the third course in the coursera Bayesian Statistics specialization. In the first course we looked at the basics of Bayesian statistics and in the second course we looked at Bayesian regression models. Now we turn our attention to mixture models, which are a simple yet powerful generalization of the models we have seen so far. Mixtures are distributions consisting of weighted sums of distributions. The idea dates back to the work of Karl Pearson in 1894, who used mixtures to model the distribution of heights in a population.
Mixture models are widely used in various fields, including machine learning, statistics, and data science.
We will cover the following topics:
Basic Concepts: Understanding the fundamental ideas behind mixture models, including components, weights, and the overall mixture distribution.
Bayesian Inference: Learning how to perform Bayesian inference in the context of mixture models, including the use of Markov Chain Monte Carlo (MCMC) methods.
Applications: Exploring various applications of mixture models in real-world scenarios, such as clustering, density estimation, and anomaly detection.
By the end of this course, you will have a solid understanding of mixture models and their applications in Bayesian statistics.
📐 What we don’t cover
In the next course we will look at time series models and in the final course we will also consider using mixture models for time series data.
Although this specialization does not cover Gaussian processes, mixtures are a special case of Gaussian processes and can help us develop some of the intuition behind them. Another omission is that mixture models are the advanced version called mixture of experts which are used in deep learning.
If possible I’d like to look into the above topics using material from some textbooks below.
🤯 The Instructor
The course comes with extensive notes by Abel Rodríguez.
Rodríguez is associated with Nimble, a system for programming and simulating hierarchical models in R. Nimble is a powerful tool for Bayesian modeling and inference, and it is particularly well-suited for mixture models. And is compatible with JAGS
He co-authored “Probability, Decisions, and Games: A Gentle Introduction Using R” an introduction to probability and decision theory using R.
✍️ References
As I pointed out above I’m also interested in mixtures of experts and Gaussian processes. The following books are good references for these topics:
- “Gaussian Processes for Machine Learning” by Carl Edward Rasmussen and Christopher K. I. Williams
- “Mixture Models: Inference and Applications” by Geoffrey McLachlan and David Peel