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Bayesian Statistics: Mixture Models · LearnSpace
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Bayesian Statistics: Mixture Models

Курс от University of California, Santa Cruz
Средний≈ 21.5 чАнглийский
О курсеНавыкиПрограммаПреподаватели

О курсе

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.

Навыки, которые вы освоите

Bayesian StatisticsStatistical ModelingProbability DistributionR ProgrammingStatistical InferenceR (Software)Statistical SoftwareMarkov ModelProbability & StatisticsStatistical MethodsMathematical ModelingSampling (Statistics)Classification Algorithms

Программа курса

5 модулей · 76 учебных материалов

01Basic concepts on Mixture Models26 материалов

Introduction

Welcome to Bayesian Statistics: Mixture ModelsВидео

The R Environment for Statistical Computing

Installing and using RВидеоAn Introduction to RЧтение

Definition of mixture models

Basic definitionsВидео

Учитесь у экспертов

Abel Rodriguez

Professor

Bayesian Statistics: Mixture Models
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Обучение на Coursera

≈ 21.5 ч

5 модулей

Язык: Английский

Субтитры: Арабский, Французский, Узбекский, Украинский, Китайский (Китай), Греческий, Итальянский, Бразильский португальский, Нидерландский, Корейский, Немецкий, Русский, Тайский, Индонезийский, Шведский, Турецкий, Испанский, Хинди, Японский, Казахский, Польский

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Basic definitionsЗадание
Mixtures of GaussiansВидео
Example of a bimodal mixture of GaussiansЧтение
Example of a unimodal and skewed mixture of GaussiansЧтение
Example of a unimodal, symmetric and heavy tailed mixture of GaussiansЧтение
Mixtures of GaussiansЗадание
When are mixture models helpful?Обсуждение
Zero-inflated mixturesВидео
Example of a zero-inflated negative binomial distributionЧтение
Example of a zero-inflated log Gaussian distributionЧтение
Zero-inflated distributionsЗадание
Definition of Mixture ModelsЗадание

Likelihood function for mixture models

Hierarchical representationsВидеоSampling from a mixture modelВидеоSample code for simulating from a Mixture ModelЧтениеThe likelihood functionВидеоThe likelihood functionЗаданиеParameter identifiabilityВидеоIdentifiabilityЗаданиеLikelihood function for mixture modelsЗадание

Advanced simulation and likelihood function

Simulating from a Mixture ModelВзаимная проверкаLikelihood function for mixture modelsВзаимная проверка
02Maximum likelihood estimation for Mixture Models9 материалов

The EM algorithm for Mixture Models

EM for general mixturesВидеоEM for location mixtures of GaussiansВидеоEM example 1ВидеоSample code for EM example 1ЧтениеEM example 2ВидеоSample code for EM example 2ЧтениеMixtures of log-GaussiansОбсуждение

Advanced EM algorithm

The EM algorithm for zero-inflated mixturesВзаимная проверкаThe EM algorithm for Mixture ModelsВзаимная проверка
03Bayesian estimation for Mixture Models10 материалов

Markov chain Monte Carlo algorithms for Mixture Models

Markov Chain Monte Carlo algorithms part 1ВидеоMarkov Chain Monte Carlo algorithms, part 2ВидеоMCMC for location mixtures of normals Part 1ВидеоMCMC for location mixtures of normals Part 2ВидеоMCMC Example 1ВидеоSample code for MCMC example 1ЧтениеMCMC Example 2ВидеоSample code for MCMC example 2Чтение

Advanced MCMC

The MCMC algorithm for zero-inflated mixturesВзаимная проверкаMarkov chain Monte Carlo algorithms for Mixture ModelsВзаимная проверка
04Applications of Mixture Models13 материалов

Density estimation

Density estimation using Mixture ModelsВидеоDensity Estimation ExampleВидеоSample code for density estimation problemsЧтение

Clustering

Mixture Models for ClusteringВидеоClustering exampleВидеоSample EM algorithm for clustering problemsЧтение

Classification

Mixture Models and naive Bayes classifiersВидеоLinear and quadratic discriminant analysis in the context of Mixture ModelsВидеоClassification exampleВидеоSample EM algorithm for classification problemsЧтение

Advanced Density Estimation and Classification

The EM algorithm and density estimationВзаимная проверкаMCMC algorithms and density estimationВзаимная проверкаClassificationВзаимная проверка
05Practical considerations18 материалов

Computational considerations for Mixture Models

Numerical stabilityВидеоSample code to illustrate numerical stability issuesЧтениеComputational issues associated with multimodalityВидеоSample code to illustrate multimodality issues 1ЧтениеSample code to illustrate multimodality issues 2ЧтениеComputational considerations for Mixture ModelsЗадание

Determining the number of components in a Mixture Model

Bayesian Information Criteria (BIC)ВидеоBayesian Information Criteria (BIC)ЗаданиеBayesian Information Criteria ExampleВидеоSample code: Bayesian Information CriteriaЧтениеEstimating the number of components in Bayesian settingsВидеоEstimating the number of components in Bayesian settingsЗадание

Advanced BIC

BIC for zero-inflated mixturesВзаимная проверка
Estimating the full partition structure in Bayesian settingsВидео
Simplifying Binder's expected loss functionОбсуждение
Example: Bayesian inference for the partition structureВидео
Sample code for estimating the number of components and the partition structure in Bayesian modelsЧтение
Estimating the partition structure in Bayesian modelsЗадание