A rigorous introduction to the theory of Bayesian Statistical Inference and Data Analysis, including prior and posterior distributions, Bayesian estimation and testing, Bayesian computation theories and methods, and implementation of Bayesian computation methods using popular statistical software.
Required Textbook: Gelman, A., Carlin, J. B., Stern, H. S., Rubin, D. B. (2013) Bayesian Data
Analysis, Third Edition, Chapman & Hall/CRC.
Software Requirements: R or Python, Word processing (such as Word, Pages, LaTeX, etc)
Welcome to MATH 574 Bayesian Computational Statistics! This module covers the ideas of Bayesian inference. It focuses on a framework for Bayesian inference and discusses the general approach to computation.
涵盖的内容
11个视频5篇阅读材料4个作业1个讨论话题1个非评分实验室
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11个视频•总计71分钟
Course Overview•6分钟
Instructor Introduction•3分钟
Module 1 Introduction•2分钟
Bayes' rule and its consequences Pt. 1•7分钟
Bayes' rule and its consequences Pt. 2•11分钟
Fundamentals of Bayesian inference Pt. 1•10分钟
Fundamentals of Bayesian inference Pt. 2•10分钟
Fundamentals of Bayesian inference Pt. 3•2分钟
Fundamentals of Bayesian inference Pt. 4•10分钟
Bayesian Computation Pt. 1•7分钟
Bayesian Computation Pt. 2•4分钟
5篇阅读材料•总计260分钟
Syllabus•10分钟
Bayesian Probability Readings•60分钟
Bayesian Reading•120分钟
Computation Reading•60分钟
Module 1 Summary•10分钟
4个作业•总计165分钟
Bayesian Probability Quiz•15分钟
Bayesian Inference Quiz•15分钟
Computation Quiz•15分钟
Module 1 Summative Assessment•120分钟
1个讨论话题•总计10分钟
Meet and Greet Discussion•10分钟
1个非评分实验室•总计60分钟
Module 1 - Lesson 3 - RStudio Lab•60分钟
Module 2: Single Parameter Models
第 2 单元•小时 后完成
单元详情
This module equips students with a solid foundation in Bayesian inference for single parameter models, emphasizing both theoretical understanding and practical application.
涵盖的内容
17个视频4篇阅读材料4个作业1个非评分实验室
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17个视频•总计117分钟
Module 2 Introduction•1分钟
Binomial and Posterior Distributions Pt. 1•6分钟
Binomial and Posterior Distributions Pt. 2•7分钟
Binomial and Posterior Distributions Pt. 3•9分钟
Binomial and Posterior Distributions Pt. 4•9分钟
Binomial and Posterior Distributions Pt. 5•4分钟
Binomial and Posterior Distributions Pt. 6•6分钟
Priors Pt. 1•9分钟
Priors Pt. 2•8分钟
Priors Pt. 3•5分钟
Other Single-Parameter Models Pt. 1•2分钟
Other Single-Parameter Models Pt. 2•10分钟
Other Single-Parameter Models Pt. 3•8分钟
Other Single-Parameter Models Pt. 4•9分钟
Other Single-Parameter Models Pt. 5•4分钟
Other Single-Parameter Models Pt. 6•9分钟
Other Single-Parameter Models Pt. 7•11分钟
4篇阅读材料•总计370分钟
Estimating Probabilities and Posterior Distributions Readings•120分钟
Summarizing Posterior Inference and Prior Distributions Readings•120分钟
Normal Distribution and Other Single-Parameter Models Reading•120分钟
Module 2 Summary•10分钟
4个作业•总计165分钟
Estimating Probabilities and Posterior Quiz•15分钟
Summarizing Posterior Inference and Prior Distributions Quiz•15分钟
Normal Distribution and Other Single-Parameter Models Quiz•15分钟
Module 2 Summative Assessment•120分钟
1个非评分实验室•总计60分钟
Module 2 - Lesson 3 - RStudio Lab•60分钟
Module 3: Multiparameter Models
第 3 单元•小时 后完成
单元详情
This module provides an overview of Bayesian inference for multiparameter models, focusing on handling normal data, employing conjugate priors, and applying multivariate normal models to practical scenarios.
涵盖的内容
13个视频5篇阅读材料4个作业3个非评分实验室
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13个视频•总计110分钟
Module 3 Introduction•1分钟
Nuisance Parameters Pt. 1•10分钟
Nuisance Parameters Pt. 2•11分钟
Nuisance Parameters Pt. 3•8分钟
Nuisance Parameters Pt. 4•10分钟
Nuisance Parameters Pt. 5•10分钟
Nuisance Parameters Pt. 6•10分钟
Nuisance Parameters Pt. 7•10分钟
Conjugate Priors Pt. 1•9分钟
Conjugate Priors Pt. 2•5分钟
Conjugate Priors Pt. 3•7分钟
More Models and Applications Pt. 1•9分钟
More Models and Applications Pt. 2•10分钟
5篇阅读材料•总计200分钟
Multiparameter Models Reading•60分钟
Conjugate Priors and Multivariate Normal Models Readings•60分钟
Advanced Multivariate Models and Practical Applications Reading•60分钟
Module 3 Summary•10分钟
Insights from an Industry Leader: Learn More About Our Program•10分钟
4个作业•总计165分钟
Handling Normal Data and Nuisance Parameters Quiz•15分钟
Conjugate Priors and Multivariate Normal Models Quiz•15分钟
Advanced Multivariate Models and Practical Applications Quiz•15分钟
Module 3 Summative Assessment•120分钟
3个非评分实验室•总计180分钟
Module 3 - Lesson 1 - RStudio Lab•60分钟
Module 3 - Lesson 2 - RStudio Lab•60分钟
Module 3 - Lesson 3 - RStudio Lab•60分钟
Module 4: Large-Sample Inference and Frequency Properties
第 4 单元•小时 后完成
单元详情
This module provides an understanding of large-sample inference and frequency properties in Bayesian analysis, focusing on normal approximations, large-sample theory, and the evaluation of Bayesian methods from a frequentist perspective.
涵盖的内容
14个视频4篇阅读材料4个作业1个非评分实验室
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14个视频•总计101分钟
Module 4 Introduction•1分钟
Normal Approximation Pt. 1•9分钟
Normal Approximation Pt. 2•8分钟
Normal Approximation Pt. 3•8分钟
Normal Approximation Pt. 4•9分钟
Normal Approximation Pt. 5•6分钟
Large-Sample Theory Pt. 1•8分钟
Large-Sample Theory Pt. 2•9分钟
Large-Sample Theory Pt. 3•5分钟
Large-Sample Theory Pt. 4•9分钟
Large-Sample Theory Pt. 5•7分钟
Large-Sample Theory Pt. 6•6分钟
Frequency Properties Pt. 1•8分钟
Frequency Properties Pt. 2•7分钟
4篇阅读材料•总计310分钟
Normal Approximation and Its Applications Reading•60分钟
Exploring Large-Sample Theory and Counterexamples Readings•120分钟
Frequency Properties and Broader Interpretations of Bayesian Readings•120分钟
Module 4 Summary•10分钟
4个作业•总计165分钟
Normal Approximation and Its Applications Quiz•15分钟
Exploring Large-Sample Theory and Counterexamples Quiz•15分钟
Frequency Properties and Broader Interpretations of Bayesian Methods Quiz•15分钟
Module 4 Summative Assessment•120分钟
1个非评分实验室•总计60分钟
Module 4 - Lesson 1 - RStudio Lab•60分钟
Module 5: Hierarchical Models
第 5 单元•小时 后完成
单元详情
This module provides an overview of hierarchical models within Bayesian inference, focusing on constructing priors, understanding exchangeability, performing analysis, and ensuring model validity and improvement.
涵盖的内容
9个视频4篇阅读材料4个作业1个非评分实验室
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9个视频•总计46分钟
Module 5 Introduction•1分钟
Parameterized Priors and Exchangeability Pt. 1•6分钟
Parameterized Priors and Exchangeability Pt. 2•6分钟
Hierarchical Models Pt. 1•4分钟
Hierarchical Models Pt. 2•4分钟
Hierarchical Models Pt. 3•4分钟
Hierarchical Models Pt. 4•8分钟
Model Validation Pt. 1•4分钟
Model Validation Pt. 2•8分钟
4篇阅读材料•总计370分钟
Parameterized Priors and the Concept of Exchangeability Readings•60分钟
Analysis and Applications of Hierarchical Models Readings•180分钟
Computational Techniques and Model Validation Reading•120分钟
Module 5 Summary•10分钟
4个作业•总计165分钟
Parameterized Priors and the Concept of Exchangeability Quiz•15分钟
Analysis and Applications of Hierarchical Models Quiz•15分钟
Computational Techniques and Model Validation Quiz•15分钟
Module 5 Summative Assessment•120分钟
1个非评分实验室•总计60分钟
Module 5 - Lesson 3 - RStudio Lab•60分钟
Module 6: Bayesian Computation
第 6 单元•小时 后完成
单元详情
This module provides a comprehensive understanding of Bayesian computation techniques, emphasizing numerical integration, simulation methods, and advanced Markov chain algorithms. Students will gain practical skills in implementing these methods and debugging computational issues.
涵盖的内容
12个视频4篇阅读材料4个作业1个非评分实验室
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12个视频•总计75分钟
Module 6 Introduction•1分钟
Numerical Methods and Approximation Pt. 1•4分钟
Numerical Methods and Approximation Pt. 2•4分钟
Numerical Methods and Approximation Pt. 3•3分钟
Simulation Techniques for Bayesian Inference Pt. 1•7分钟
Simulation Techniques for Bayesian Inference Pt. 2•10分钟
Simulation Techniques for Bayesian Inference Pt. 3•9分钟
Simulation Techniques for Bayesian Inference Pt. 4•7分钟
Markov Chain Methods Pt. 1•7分钟
Markov Chain Methods Pt. 2•7分钟
Markov Chain Methods Pt. 3•5分钟
Markov Chain Methods Pt. 4•10分钟
4篇阅读材料•总计430分钟
Numerical Methods and Approximations in Bayesian Computation Readings•60分钟
Simulation Techniques for Bayesian Inference Readings•120分钟
Advanced Markov Chain Methods for Bayesian Computation Readings•240分钟
Module 6 Summary•10分钟
4个作业•总计165分钟
Numerical Methods and Approximations in Bayesian Computation Quiz•15分钟
Simulation Techniques for Bayesian Inference Quiz•15分钟
Advanced Markov Chain Methods for Bayesian Computation Quiz•15分钟
Module 6 Summative Assessment•120分钟
1个非评分实验室•总计60分钟
Module 6 - Lesson 3 - RStudio Lab•60分钟
Module 7: Regression Models
第 7 单元•小时 后完成
单元详情
This module consists of an overview of regression models in Bayesian inference, focusing on foundational principles, hierarchical linear models, and generalized linear models, with practical applications and advanced techniques.
涵盖的内容
19个视频4篇阅读材料4个作业1个非评分实验室
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19个视频•总计97分钟
Module 7 Introduction•1分钟
Foundations of Bayesian Regression Analysis Pt. 1•4分钟
Foundations of Bayesian Regression Analysis Pt. 2•4分钟
Foundations of Bayesian Regression Analysis Pt. 3•7分钟
Foundations of Bayesian Regression Analysis Pt. 4•4分钟
Foundations of Bayesian Regression Analysis Pt. 5•6分钟
Foundations of Bayesian Regression Analysis Pt. 6•7分钟
Foundations of Bayesian Regression Analysis Pt. 7•7分钟
Hierarchical Linear Models Pt. 1•8分钟
Hierarchical Linear Models Pt. 2•7分钟
Hierarchical Linear Models Pt. 3•11分钟
Hierarchical Linear Models Pt. 4•4分钟
Generalized Linear Models Pt. 1•2分钟
Generalized Linear Models Pt. 2•2分钟
Generalized Linear Models Pt. 3•2分钟
Generalized Linear Models Pt. 4•4分钟
Generalized Linear Models Pt. 5•3分钟
Generalized Linear Models Pt. 6•7分钟
Generalized Linear Models Pt. 7•8分钟
4篇阅读材料•总计370分钟
Foundations of Bayesian Regression Analysis Readings•240分钟
Advanced Techniques in Hierarchical Linear Models Readings•60分钟
Exploring Generalized Linear Models in Bayesian Context Readings•60分钟
Module 7 Summary•10分钟
4个作业•总计165分钟
Foundations of Bayesian Regression Analysis Quiz•15分钟
Advanced Techniques in Hierarchical Linear Models Quiz•15分钟
Exploring Generalized Linear Models in Bayesian Context Quiz•15分钟
Module 7 Summative Assessment•120分钟
1个非评分实验室•总计60分钟
Module 7 - Lesson 3 - RStudio Lab•60分钟
Module 8: Advanced Topics
第 8 单元•小时 后完成
单元详情
This module covers advanced topics in Bayesian inference, focusing on the setup, interpretation, and application of mixture models, as well as addressing computational challenges and integrating mixture models with multivariate data analysis.
涵盖的内容
9个视频3篇阅读材料3个作业1个非评分实验室
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9个视频•总计48分钟
Module 8 Introduction•1分钟
Setting Up and Interpreting Mixture Models Pt. 1•8分钟
Setting Up and Interpreting Mixture Models Pt. 2•6分钟
Setting Up and Interpreting Mixture Models Pt. 3•3分钟
Setting Up and Interpreting Mixture Models Pt. 4•3分钟
Setting Up and Interpreting Mixture Models Pt. 5•4分钟
Applications of Mixture Models Pt. 1•9分钟
Applications of Mixture Models Pt. 2•6分钟
Applications of Mixture Models Pt. 3•8分钟
3篇阅读材料•总计250分钟
Setting Up and Interpreting Mixture Models Readings•60分钟
Practical Applications and Computational Challenges Readings•180分钟
Module 8 Summary•10分钟
3个作业•总计150分钟
Setting Up and Interpreting Mixture Models Quiz•15分钟
Practical Applications and Computational Challenges Quiz•15分钟
Module 8 Summative Assessment •120分钟
1个非评分实验室•总计60分钟
Module 8 - Lesson 2 - RStudio Lab•60分钟
Summative Course Assessment
第 9 单元•小时 后完成
单元详情
This module contains the summative course assessment that has been designed to evaluate your understanding of the course material and assess your ability to apply the knowledge you have acquired throughout the course.
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