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.

Bayesian Computational Statistics
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中级
Probability and statistics at the graduate level.
Prior exposure to simulation, MCMC methods, and R programming recommended.
推荐体验
推荐体验
中级
Probability and statistics at the graduate level.
Prior exposure to simulation, MCMC methods, and R programming recommended.
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32 项作业
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该课程共有9个模块
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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.
涵盖的内容
1个作业
1个作业• 总计180分钟
- Summative Course Assessment• 180分钟
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攻读学位
课程 是 Illinois Tech提供的以下学位课程的一部分。如果您被录取并注册,您已完成的课程可计入您的学位学习,您的学习进度也可随之转移。
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Master of Data Science
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