UCSC - Bayesian Statistics: Mixture Models
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Bayesian Statistics: Mixture Models at Coursera Overview
Duration | 22 hours |
Start from | Start Now |
Total fee | Free |
Mode of learning | Online |
Difficulty level | Intermediate |
Official Website | Explore Free Course  |
Credential | Certificate |
Bayesian Statistics: Mixture Models at Coursera Highlights
- Earn a shareable certificate upon completion.
- Flexible deadlines according to your schedule.
Bayesian Statistics: Mixture Models at Coursera Course details
- 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.
Bayesian Statistics: Mixture Models at Coursera Curriculum
Basic concepts on Mixture Models
Welcome to Bayesian Statistics: Mixture Models
Installing and using R
Basic definitions
Mixtures of Gaussians
Zero-inflated mixtures
Hierarchical representations
Sampling from a mixture model
The likelihood function
Parameter identifiability
An Introduction to R
Example of a bimodal mixture of Gaussians
Example of a unimodal and skewed mixture of Gaussians
Example of a unimodal, symmetric and heavy tailed mixture of Gaussians
Example of a zero-inflated negative binomial distribution
Example of a zero-inflated log Gaussian distribution
Sample code for simulating from a Mixture Model
Basic definitions
Mixtures of Gaussians
Zero-inflated distributions
Definition of Mixture Models
The likelihood function
Identifiability
Likelihood function for mixture models
Maximum likelihood estimation for Mixture Models
EM for general mixtures
EM for location mixtures of Gaussians
EM example 1
EM example 2
Sample code for EM example 1
Sample code for EM example 2
Bayesian estimation for Mixture Models
Markov Chain Monte Carlo algorithms part 1
Markov Chain Monte Carlo algorithms, part 2
MCMC for location mixtures of normals Part 1
MCMC for location mixtures of normals Part 2
MCMC Example 1
MCMC Example 2
Sample code for MCMC example 1
Sample code for MCMC example 2
Applications of Mixture Models
Density estimation using Mixture Models
Density Estimation Example
Mixture Models for Clustering
Clustering example
Mixture Models and naive Bayes classifiers
Linear and quadratic discriminant analysis in the context of Mixture Models
Classification example
Sample code for density estimation problems
Sample EM algorithm for clustering problems
Sample EM algorithm for classification problems
Practical considerations
Numerical stability
Computational issues associated with multimodality
Bayesian Information Criteria (BIC)
Bayesian Information Criteria Example
Estimating the number of components in Bayesian settings
Estimating the full partition structure in Bayesian settings
Example: Bayesian inference for the partition structure
Sample code to illustrate numerical stability issues
Sample code to illustrate multimodality issues 1
Sample code to illustrate multimodality issues 2
Sample code: Bayesian Information Criteria
Sample code for estimating the number of components and the partition structure in Bayesian models
Computational considerations for Mixture Models
Bayesian Information Criteria (BIC)
Estimating the number of components in Bayesian settings
Estimating the partition structure in Bayesian models
Bayesian Statistics: Mixture Models at Coursera Admission Process
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