Bayesian Statistics: Mixture Models

University of California, Santa Cruz

About this Course

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Bayesian Statistics: Mixture Models introduces you to an important class of statistical models. The course is organized in five modules, each of which contains lecture videos, short quizzes, background reading, discussion prompts, and one or more peer-reviewed assignments. Statistics is best learned by doing it, not just watching a video, so the course is structured to help you learn through application. 
Some exercises require the use of R, a freely-available statistical software package. A brief tutorial is provided, but we encourage you to take advantage of the many other resources online for learning R if you are interested.

This is an advanced course, and it was designed to be the third in UC Santa Cruz's series on Bayesian statistics, after Herbie Lee's "Bayesian Statistics: From Concept to Data Analysis" and Matthew Heiner's "Bayesian Statistics: Techniques and Models." To succeed in the course, you should have some knowledge of and comfort with calculus-based probability, principles of maximum-likelihood estimation, and Bayesian estimation.

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Advanced Level

Approx. 22 hours to complete

English

Subtitles: French, Portuguese (European), Russian, English, Spanish

Instructor

Instructor rating

5/5 (6 Ratings)

Abel Rodriguez

Professor

Applied Mathematics and Statistics

3,520 Learners

1 Course

Shareable Certificate

Earn a Certificate upon completion

100% online

Start instantly and learn at your own schedule.

Flexible deadlines

Reset deadlines in accordance to your schedule.

Advanced Level

Approx. 22 hours to complete

English

Subtitles: French, Portuguese (European), Russian, English, Spanish

Offered by

University of California, Santa Cruz

UC Santa Cruz is an outstanding public research university with a deep commitment to undergraduate education. It’s a place that connects people and programs in unexpected ways while providing unparalleled opportunities for students to learn through hands-on experience.

Syllabus - What you will learn from this course

Week

Week 1

4 hours to complete

Basic concepts on Mixture Models

This module defines mixture models, discusses its properties, and develops the likelihood function for a random sample from a mixture model that will be the basis for statistical learning.

4 hours to complete

9 videos (Total 94 min), 7 readings, 9 quizzes

9 videos

Welcome to Bayesian Statistics: Mixture Models3m

Installing and using R5m

Basic definitions25m

Mixtures of Gaussians10m

Zero-inflated mixtures11m

Hierarchical representations7m

Sampling from a mixture model5m

The likelihood function14m

Parameter identifiability10m

7 readings

An Introduction to R45m

Example of a bimodal mixture of Gaussians3m

Example of a unimodal and skewed mixture of Gaussians3m

Example of a unimodal, symmetric and heavy tailed mixture of Gaussians3m

Example of a zero-inflated negative binomial distribution3m

Example of a zero-inflated log Gaussian distribution3m

Sample code for simulating from a Mixture Model10m

7 practice exercises

Basic definitions6m

Mixtures of Gaussians4m

Zero-inflated distributions4m

Definition of Mixture Models20m

The likelihood function

Identifiability

Likelihood function for mixture models4m

Week

Week 2

4 hours to complete

Maximum likelihood estimation for Mixture Models

4 hours to complete

4 videos (Total 73 min), 2 readings, 2 quizzes

4 videos

EM for general mixtures24m

EM for location mixtures of Gaussians22m

EM example 112m

EM example 213m

2 readings

Sample code for EM example 110m

Sample code for EM example 210m

Week

Week 3

4 hours to complete

Bayesian estimation for Mixture Models

4 hours to complete

6 videos (Total 84 min), 2 readings, 2 quizzes

6 videos

Markov Chain Monte Carlo algorithms part 112m

Markov Chain Monte Carlo algorithms, part 213m

MCMC for location mixtures of normals Part 119m

MCMC for location mixtures of normals Part 214m

MCMC Example 111m

MCMC Example 211m

2 readings

Sample code for MCMC example 110m

Sample code for MCMC example 210m

Week

Week 4

5 hours to complete

Applications of Mixture Models

5 hours to complete

7 videos (Total 108 min), 3 readings, 3 quizzes

7 videos

Density estimation using Mixture Models12m

Density Estimation Example10m

Mixture Models for Clustering23m

Clustering example11m

Mixture Models and naive Bayes classifiers21m

Linear and quadratic discriminant analysis in the context of Mixture Models18m

Classification example10m

3 readings

Sample code for density estimation problems10m

Sample EM algorithm for clustering problems10m

Sample EM algorithm for classification problems10m

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Bayesian Statistics: Mixture Models

Bayesian Statistics: Mixture Models