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Bayesian Statistics

Курс от Duke University
Средний≈ 34.7 чАнглийский
О курсеНавыкиПрограммаПреподаватели

О курсе

This course describes Bayesian statistics, in which one's inferences about parameters or hypotheses are updated as evidence accumulates. You will learn to use Bayes’ rule to transform prior probabilities into posterior probabilities, and be introduced to the underlying theory and perspective of the Bayesian paradigm. The course will apply Bayesian methods to several practical problems, to show end-to-end Bayesian analyses that move from framing the question to building models to eliciting prior probabilities to implementing in R (free statistical software) the final posterior distribution. Additionally, the course will introduce credible regions, Bayesian comparisons of means and proportions, Bayesian regression and inference using multiple models, and discussion of Bayesian prediction. We assume learners in this course have background knowledge equivalent to what is covered in the earlier three courses in this specialization: "Introduction to Probability and Data," "Inferential Statistics," and "Linear Regression and Modeling."

Навыки, которые вы освоите

Bayesian StatisticsProbability DistributionProbabilityRegression AnalysisStatistical ModelingModel EvaluationPredictive ModelingStatistical InferenceData AnalysisData-Driven Decision-MakingStatistical ProgrammingStatistical SoftwareR ProgrammingStatistical MethodsAnalysisStatistical Hypothesis TestingProbability & StatisticsStatistical Analysis

Программа курса

7 модулей · 82 учебных материалов

01About the Specialization and the Course6 материалов

Overview

Introduction to Statistics with RВидеоAbout Statistics with R SpecializationЧтениеAbout Bayesian StatisticsЧтениеPre-requisite KnowledgeЧтение

Учитесь у экспертов

Mine Çetinkaya-Rundel

Associate Professor of the Practice

David Banks

Professor of the Practice

Colin Rundel

Assistant Professor of the Practice

Merlise A Clyde

Professor

Bayesian Statistics
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≈ 34.7 ч

7 модулей

Язык: Английский

Субтитры: Арабский, Французский, Бенгальский, Украинский, Китайский (Китай), Греческий, Итальянский, Бразильский португальский, Вьетнамский, Нидерландский, Корейский, Немецкий, Пушту, Урду, Русский, Тайский, Индонезийский, Шведский, Турецкий, Азербайджанский, Испанский, Дари, Хинди, Японский, Казахский, Венгерский, Польский

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02The Basics of Bayesian Statistics16 материалов

Introduction to Bayesian Statistics

The Basics of Bayesian StatisticsВидеоModule Learning ObjectivesЧтение

Bayes' Rule

Conditional Probabilities and Bayes' RuleВидеоBayes' Rule and Diagnostic TestingВидеоBayes UpdatingВидеоBayesian vs. frequentist definitions of probabilityВидео

Inference for a Proportion

Inference for a Proportion: Frequentist ApproachВидеоInference for a Proportion: Bayesian ApproachВидеоEffect of Sample Size on the PosteriorВидео

Frequentist vs. Bayesian Inference

Frequentist vs. Bayesian InferenceВидео

Learning R

About Lab ChoicesЧтениеWeek 1 Lab Instructions (RStudio)ЧтениеWeek 1 Lab Instructions (RStudio Cloud)ЧтениеWeek 1 LabЗадание

Strengthen Your Understanding

Week 1 Practice QuizЗаданиеWeek 1 QuizЗадание
03Bayesian Inference16 материалов

Introduction to Bayesian Inference

Bayesian InferenceВидеоModule Learning ObjectivesЧтение

Continuous Variables and Eliciting Probability Distributions

From the Discrete to the ContinuousВидеоElicitationВидеоConjugacyВидео

Three Conjugate Families

Inference on a Binomial ProportionВидеоThe Gamma-Poisson Conjugate FamiliesВидеоThe Normal-Normal Conjugate FamiliesВидео

Credible Intervals and Predictive Inference

Non-Conjugate PriorsВидеоCredible IntervalsВидеоPredictive InferenceВидео

Learning R

Week 2 Lab Instructions (RStudio)ЧтениеWeek 1 Lab Instructions (RStudio Cloud)ЧтениеWeek 2 LabЗадание

Strengthen Your Understanding

Week 2 Practice QuizЗаданиеWeek 2 QuizЗадание
04Decision Making20 материалов

Decision Making

Decision makingВидеоModule Learning ObjectivesЧтение

Losses and Decision Making

Losses and decision makingВидеоWorking with loss functionsВидеоMinimizing expected loss for hypothesis testingВидеоPosterior probabilities of hypotheses and Bayes factorsВидео

Inference for Normal Data

The Normal-Gamma Conjugate FamilyВидеоInference via Monte Carlo SamplingВидеоPredictive Distributions and Prior ChoiceВидеоReference PriorsВидеоMixtures of Conjugate Priors and MCMCВидео

Comparing Normal Means and Testing Hypotheses

Hypothesis Testing: Normal Mean with Known VarianceВидеоComparing Two Paired Means Using Bayes' FactorsВидеоComparing Two Independent Means: Hypothesis TestingВидеоComparing Two Independent Means: What to Report?Видео

Learning R

Week 3 Lab Instructions (RStudio)ЧтениеWeek 3 Lab Instructions (RStudio Cloud)ЧтениеWeek 3 LabЗадание

Strengthen Your Understanding

Week 3 Practice QuizЗаданиеWeek 3 QuizЗадание
05Bayesian Regression17 материалов

Introducing Bayesian Regression

Bayesian regressionВидеоModule Learning ObjectivesЧтение

Simple and Multiple Bayesian Regressions

Bayesian simple linear regressionВидеоChecking for outliersВидеоBayesian multiple regressionВидео

Bayesian Model Uncertainty and Model Averaging

Model selection criteriaВидеоBayesian model uncertaintyВидеоBayesian model averagingВидео

Markov Chain Monte Carlo

Stochastic explorationВидеоPriors for Bayesian model uncertaintyВидеоR demo: crime and punishmentВидеоDecisions under model uncertaintyВидео

Learning R

Week 4 Lab Instructions (RStudio Cloud)ЧтениеWeek 4 Lab Instructions (RStudio Cloud)ЧтениеWeek 4 LabЗадание

Strengthen Your Understanding

Week 4 Practice QuizЗаданиеWeek 4 QuizЗадание
06Perspectives on Bayesian Applications4 материалов

Interviews

About this moduleЧтениеBayesian inference: a talk with Jim BergerВидеоBayesian methods and big data: a talk with David DunsonВидеоBayesian methods in biostatistics and public health: a talk with Amy HerringВидео
07Data Analysis Project3 материалов

Peer Review Project

Project informationЧтениеData Analysis ProjectВзаимная проверкаShare your learning experienceЧтение