Bayesian Statistics: Techniques and Models

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About this course: This is the second of a two-course sequence introducing the fundamentals of Bayesian statistics. It builds on the course Bayesian Statistics: From Concept to Data Analysis, which introduces Bayesian methods through use of simple conjugate models. Real-world data often require more sophisticated models to reach realistic conclusions. This course aims to expand our “Bayesian toolbox” with more general models, and computational techniques to fit them. In particular, we will introduce Markov chain Monte Carlo (MCMC) methods, which allow sampling from posterior distributions that have no analytical solution. We will use the open-source, freely available software R (some ex…

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When you enroll for courses through Coursera you get to choose for a paid plan or for a free plan

  • Free plan: No certicification and/or audit only. You will have access to all course materials except graded items.
  • Paid plan: Commit to earning a Certificate—it's a trusted, shareable way to showcase your new skills.

About this course: This is the second of a two-course sequence introducing the fundamentals of Bayesian statistics. It builds on the course Bayesian Statistics: From Concept to Data Analysis, which introduces Bayesian methods through use of simple conjugate models. Real-world data often require more sophisticated models to reach realistic conclusions. This course aims to expand our “Bayesian toolbox” with more general models, and computational techniques to fit them. In particular, we will introduce Markov chain Monte Carlo (MCMC) methods, which allow sampling from posterior distributions that have no analytical solution. We will use the open-source, freely available software R (some experience is assumed, e.g., completing the previous course in R) and JAGS (no experience required). We will learn how to construct, fit, assess, and compare Bayesian statistical models to answer scientific questions involving continuous, binary, and count data. This course combines lecture videos, computer demonstrations, readings, exercises, and discussion boards to create an active learning experience. The lectures provide some of the basic mathematical development, explanations of the statistical modeling process, and a few basic modeling techniques commonly used by statisticians. Computer demonstrations provide concrete, practical walkthroughs. Completion of this course will give you access to a wide range of Bayesian analytical tools, customizable to your data.

Created by:  University of California, Santa Cruz
  • Taught by:  Matthew Heiner, Doctoral Student

    Applied Mathematics and Statistics
Level Intermediate Commitment 5 weeks of study, 4-6 hours/week. Language English How To Pass Pass all graded assignments to complete the course. User Ratings 4.8 stars Average User Rating 4.8See what learners said Задания курса

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Syllabus


WEEK 1


Statistical modeling and Monte Carlo estimation
Statistical modeling, Bayesian modeling, Monte Carlo estimation


11 videos, 4 readings expand


  1. Video: Course introduction
  2. Материал для самостоятельного изучения: Module 1 assignments and materials
  3. Video: Objectives
  4. Video: Modeling process
  5. Вопрос для обсуждения: Statistical modeling process
  6. Video: Components of Bayesian models
  7. Video: Model specification
  8. Video: Posterior derivation
  9. Video: Non-conjugate models
  10. Материал для самостоятельного изучения: Reference: Common probability distributions
  11. Video: Monte Carlo integration
  12. Video: Monte Carlo error and marginalization
  13. Video: Computing examples
  14. Video: Computing Monte Carlo error
  15. Материал для самостоятельного изучения: Code for Lesson 3
  16. Материал для самостоятельного изучения: Markov chains

Graded: Lesson 1
Graded: Lesson 2
Graded: Lesson 3
Graded: Markov chains

WEEK 2


Markov chain Monte Carlo (MCMC)
Metropolis-Hastings, Gibbs sampling, assessing convergence


11 videos, 7 readings expand


  1. Материал для самостоятельного изучения: Module 2 assignments and materials
  2. Video: Algorithm
  3. Video: Demonstration
  4. Video: Random walk example, Part 1
  5. Video: Random walk example, Part 2
  6. Материал для самостоятельного изучения: Code for Lesson 4
  7. Video: Download, install, setup
  8. Video: Model writing, running, and post-processing
  9. Материал для самостоятельного изучения: Alternative MCMC software
  10. Материал для самостоятельного изучения: Code from JAGS introduction
  11. Video: Multiple parameter sampling and full conditional distributions
  12. Video: Conditionally conjugate prior example with Normal likelihood
  13. Video: Computing example with Normal likelihood
  14. Материал для самостоятельного изучения: Code for Lesson 5
  15. Video: Trace plots, autocorrelation
  16. Материал для самостоятельного изучения: Autocorrelation
  17. Video: Multiple chains, burn-in, Gelman-Rubin diagnostic
  18. Материал для самостоятельного изучения: Code for Lesson 6

Graded: Lesson 4
Graded: Lesson 5
Graded: Lesson 6
Graded: MCMC

WEEK 3


Common statistical models
Linear regression, ANOVA, logistic regression, multiple factor ANOVA


11 videos, 5 readings expand


  1. Материал для самостоятельного изучения: Module 3 assignments and materials
  2. Video: Introduction to linear regression
  3. Video: Setup in R
  4. Video: JAGS model (linear regression)
  5. Video: Model checking
  6. Video: Alternative models
  7. Video: Deviance information criterion (DIC)
  8. Материал для самостоятельного изучения: Code for Lesson 7
  9. Video: Introduction to ANOVA
  10. Video: One way model using JAGS
  11. Материал для самостоятельного изучения: Code for Lesson 8
  12. Video: Introduction to logistic regression
  13. Video: JAGS model (logistic regression)
  14. Video: Prediction
  15. Вопрос для обсуждения: Why linear models?
  16. Материал для самостоятельного изучения: Code for Lesson 9
  17. Материал для самостоятельного изучения: Multiple factor ANOVA

Graded: Lesson 7 Part A
Graded: Lesson 7 Part B
Graded: Lesson 8
Graded: Lesson 9
Graded: Common models and multiple factor ANOVA

WEEK 4


Count data and hierarchical modeling
Poisson regression, hierarchical modeling


10 videos, 7 readings expand


  1. Материал для самостоятельного изучения: Module 4 assignments and materials
  2. Video: Introduction to Poisson regression
  3. Video: JAGS model (Poisson regression)
  4. Video: Predictive distributions
  5. Материал для самостоятельного изучения: Prior sensitivity analysis
  6. Материал для самостоятельного изучения: Code for Lesson 10
  7. Video: Correlated data
  8. Материал для самостоятельного изучения: Normal hierarchical model
  9. Video: Prior predictive simulation
  10. Video: JAGS model and model checking (hierarchical modeling)
  11. Video: Posterior predictive simulation
  12. Video: Linear regression example
  13. Video: Linear regression example in JAGS
  14. Материал для самостоятельного изучения: Applications of hierarchical modeling
  15. Вопрос для обсуждения: Selecting prior distributions
  16. Материал для самостоятельного изучения: Code and data for Lesson 11
  17. Материал для самостоятельного изучения: Mixture model introduction, data, and code
  18. Video: Mixture model in JAGS

Graded: Lesson 10
Graded: Lesson 11 Part A
Graded: Lesson 11 Part B
Graded: Predictive distributions and mixture models

WEEK 5


Capstone project
Peer-reviewed data analysis project


1 video, 1 reading expand


  1. Video: Course conclusion
  2. Материал для самостоятельного изучения: Further reading and acknowledgements

Graded: Data Analysis Project

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