VOOZH about

URL: https://www.coursera.org/learn/mixture-models

⇱ Bayesian Statistics: Mixture Models | Coursera

Bayesian Statistics: Mixture Models

Keep adding new skills with 10,000+ programs for $239 (usually $399). Save now.

Bayesian Statistics: Mixture Models

This course is part of Bayesian Statistics Specialization

12,032 already enrolled

Included with

Ask Coursera

Gain insight into a topic and learn the fundamentals.
4.5

63 reviews

Intermediate level

Recommended experience

2 weeks to complete
at 10 hours a week
Flexible schedule
Learn at your own pace
Gain insight into a topic and learn the fundamentals.
4.5

63 reviews

Intermediate level

Recommended experience

2 weeks to complete
at 10 hours a week
Flexible schedule
Learn at your own pace

What you'll learn

  • Explain the basic principles behind the algorithm for fitting a mixture model.

  • Compute the expectation and variance of a mixture distribution.

  • Use mixture models to solve classification and clustering problems, and to provide density estimates.

Details to know

Shareable certificate

Add to your LinkedIn profile

Assessments

11 assignments¹

AI Graded see disclaimer
Taught in English

Build your subject-matter expertise

This course is part of the Bayesian Statistics Specialization
When you enroll in this course, you'll also be enrolled in this Specialization.
  • Learn new concepts from industry experts
  • Gain a foundational understanding of a subject or tool
  • Develop job-relevant skills with hands-on projects
  • Earn a shareable career certificate

There are 5 modules in this course

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 intermediate-level 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.

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.

What's included

9 videos7 readings7 assignments2 peer reviews1 discussion prompt

9 videos•Total 94 minutes
  • Welcome to Bayesian Statistics: Mixture Models•4 minutes
  • Installing and using R•5 minutes
  • Basic definitions•25 minutes
  • Mixtures of Gaussians•10 minutes
  • Zero-inflated mixtures•12 minutes
  • Hierarchical representations•8 minutes
  • Sampling from a mixture model•5 minutes
  • The likelihood function•15 minutes
  • Parameter identifiability•10 minutes
7 readings•Total 70 minutes
  • An Introduction to R•45 minutes
  • Example of a bimodal mixture of Gaussians•3 minutes
  • Example of a unimodal and skewed mixture of Gaussians•3 minutes
  • Example of a unimodal, symmetric and heavy tailed mixture of Gaussians•3 minutes
  • Example of a zero-inflated negative binomial distribution•3 minutes
  • Example of a zero-inflated log Gaussian distribution•3 minutes
  • Sample code for simulating from a Mixture Model•10 minutes
7 assignments•Total 38 minutes
  • Basic definitions•6 minutes
  • Mixtures of Gaussians•4 minutes
  • Zero-inflated distributions•4 minutes
  • The likelihood function•0 minutes
  • Identifiability•0 minutes
  • Definition of Mixture Models•20 minutes
  • Likelihood function for mixture models•4 minutes
2 peer reviews•Total 40 minutes
  • Likelihood function for mixture models•20 minutes
  • Simulating from a Mixture Model•20 minutes
1 discussion prompt•Total 15 minutes
  • When are mixture models helpful?•15 minutes

What's included

4 videos2 readings2 peer reviews1 discussion prompt

4 videos•Total 73 minutes
  • EM for general mixtures•24 minutes
  • EM for location mixtures of Gaussians•22 minutes
  • EM example 1•12 minutes
  • EM example 2•14 minutes
2 readings•Total 20 minutes
  • Sample code for EM example 1•10 minutes
  • Sample code for EM example 2•10 minutes
2 peer reviews•Total 120 minutes
  • The EM algorithm for Mixture Models•60 minutes
  • The EM algorithm for zero-inflated mixtures•60 minutes
1 discussion prompt•Total 10 minutes
  • Mixtures of log-Gaussians•10 minutes

What's included

6 videos2 readings2 peer reviews

6 videos•Total 84 minutes
  • Markov Chain Monte Carlo algorithms part 1•13 minutes
  • Markov Chain Monte Carlo algorithms, part 2•14 minutes
  • MCMC for location mixtures of normals Part 1•20 minutes
  • MCMC for location mixtures of normals Part 2•15 minutes
  • MCMC Example 1•11 minutes
  • MCMC Example 2•12 minutes
2 readings•Total 20 minutes
  • Sample code for MCMC example 1•10 minutes
  • Sample code for MCMC example 2•10 minutes
2 peer reviews•Total 120 minutes
  • Markov chain Monte Carlo algorithms for Mixture Models•60 minutes
  • The MCMC algorithm for zero-inflated mixtures•60 minutes

What's included

7 videos3 readings3 peer reviews

7 videos•Total 108 minutes
  • Density estimation using Mixture Models•12 minutes
  • Density Estimation Example•10 minutes
  • Mixture Models for Clustering•24 minutes
  • Clustering example•11 minutes
  • Mixture Models and naive Bayes classifiers•21 minutes
  • Linear and quadratic discriminant analysis in the context of Mixture Models•18 minutes
  • Classification example•10 minutes
3 readings•Total 30 minutes
  • Sample code for density estimation problems•10 minutes
  • Sample EM algorithm for clustering problems•10 minutes
  • Sample EM algorithm for classification problems•10 minutes
3 peer reviews•Total 155 minutes
  • MCMC algorithms and density estimation•50 minutes
  • Classification•45 minutes
  • The EM algorithm and density estimation•60 minutes

What's included

7 videos5 readings4 assignments1 peer review1 discussion prompt

7 videos•Total 91 minutes
  • Numerical stability•15 minutes
  • Computational issues associated with multimodality•12 minutes
  • Bayesian Information Criteria (BIC)•11 minutes
  • Bayesian Information Criteria Example•10 minutes
  • Estimating the number of components in Bayesian settings•10 minutes
  • Estimating the full partition structure in Bayesian settings•18 minutes
  • Example: Bayesian inference for the partition structure•16 minutes
5 readings•Total 50 minutes
  • Sample code to illustrate numerical stability issues•10 minutes
  • Sample code to illustrate multimodality issues 1•10 minutes
  • Sample code to illustrate multimodality issues 2•10 minutes
  • Sample code: Bayesian Information Criteria•10 minutes
  • Sample code for estimating the number of components and the partition structure in Bayesian models•10 minutes
4 assignments•Total 65 minutes
  • Bayesian Information Criteria (BIC)•30 minutes
  • Estimating the partition structure in Bayesian models•20 minutes
  • Computational considerations for Mixture Models•15 minutes
  • Estimating the number of components in Bayesian settings•0 minutes
1 peer review•Total 60 minutes
  • BIC for zero-inflated mixtures•60 minutes
1 discussion prompt•Total 30 minutes
  • Simplifying Binder's expected loss function•30 minutes

Earn a career certificate

Add this credential to your LinkedIn profile, resume, or CV. Share it on social media and in your performance review.

Instructor

Instructor ratings
4.5 (31 ratings)
University of California, Santa Cruz
1 Course•12,032 learners

Explore more from Data Analysis

Why people choose Coursera for their career

👁 Image

Felipe M.

Learner since 2018
"To be able to take courses at my own pace and rhythm has been an amazing experience. I can learn whenever it fits my schedule and mood."
👁 Image

Jennifer J.

Learner since 2020
"I directly applied the concepts and skills I learned from my courses to an exciting new project at work."
👁 Image

Larry W.

Learner since 2021
"When I need courses on topics that my university doesn't offer, Coursera is one of the best places to go."
👁 Image

Chaitanya A.

"Learning isn't just about being better at your job: it's so much more than that. Coursera allows me to learn without limits."

Learner reviews

  • 5 stars

    65.07%

  • 4 stars

    20.63%

  • 3 stars

    11.11%

  • 2 stars

    1.58%

  • 1 star

    1.58%

Showing 3 of 63

RL
·

Reviewed on Feb 10, 2023

I really enjoyed this course! Plenty of examples on how to use Mixture Models in a Machine Learning context. Thanks to Abel and his team for putting together such an useful course.

SM
·

Reviewed on Jan 19, 2021

I learned a lot about bayesian mixture model, expectation maximization, and MCMC algorithms and their use case in classification and clustering problems. I highly recommend this course.

CM
·

Reviewed on May 17, 2021

Definitely quite mathematical in nature. Good way to learn about expectation-maximisation algorithm.

Frequently asked questions

To access the course materials, assignments and to earn a Certificate, you will need to purchase the Certificate experience when you enroll in a course. You can try a Free Trial instead, or apply for Financial Aid. The course may offer 'Full Course, No Certificate' instead. This option lets you see all course materials, submit required assessments, and get a final grade. This also means that you will not be able to purchase a Certificate experience.

When you enroll in the course, you get access to all of the courses in the Specialization, and you earn a certificate when you complete the work. Your electronic Certificate will be added to your Accomplishments page - from there, you can print your Certificate or add it to your LinkedIn profile.

Yes. In select learning programs, you can apply for financial aid or a scholarship if you can’t afford the enrollment fee. If fin aid or scholarship is available for your learning program selection, you’ll find a link to apply on the description page.

Financial aid available,

¹ Some assignments in this course are AI-graded. For these assignments, your data will be used in accordance with Coursera's Privacy Notice.