Introduction to MCMC and Bayesian Regression via rstan
In this course, students learn how to apply Markov Chain Monte Carlo techniques (MCMC) to Bayesian statistical modeling using R and rstan.
Overview
In this course, students learn how to apply Markov Chain Monte Carlo techniques (MCMC) to Bayesian statistical modeling using R and rstan. Topics covered include Gibbs sampling and the Metropolis-Hastings method. Participants also learn how to implement linear regression (normal and t errors), Poisson regression, binary/binomial regression, and ordinal regression.
- Intermediate, Advanced
- 4 Weeks
- Expert Instructor
- Tuiton-Back Guarantee
- 100% Online
- TA Support
Learning Outcomes
Students who complete this course will learn how to apply Markov Chain Monte Carlo (MCMC) techniques using R and rstan. You will be introduced to coding for rstan and learn Bayesian methods for both linear and discrete data regressions.
- Install rstan and write code in it
- Implement rstan programs in R
- Specify priors and likelihoods to define a model
- Implement a linear regression model in rstan
- Implement logistic, Poisson, ordinal and weighted regression in rstan
Who Should Take This Course
Statisticians and analysts who need to build statistical models of data.
Our Instructors
Dr. Peter Congdon
Course Syllabus
Week 1
Using Markov Chain Monte Carlo
- Monte Carlo vs MCMC
- Estimating parameters and probabilities from complex models
- Sampling from random variables
- Gibbs sampling & full conditional densities
- Convergence
- Metropolis-Hastings method
Week 2
Introduction to Coding for rstan and Running An Analysis
- Using rstan, coding principles
- R implementations of rstan programs
- Sampling from standard densities, distributional and target + options
- Specifying priors and likelihoods to define a model
- Posterior summaries
Week 3
Bayesian Methods for Linear Regression
- Linear regression model in rstan
- Setting priors on regression coefficients and residual variances
- Extending the Normal linear model (outliers, heteroscedasticity)
- Shrinkage Priors
Week 4
Bayesian Methods for Discrete Data Regression
- Logistic regression for binary and binomial responses; using other links
- Poisson regression
- Ordinal Regression
- Weighted regression
Class Dates
2023
Instructors:
Prerequisites
Participants should have had some exposure to Bayesian computing such as that provided in our Introduction to Bayesian Computing course, and familiarity with generalized linear models, such as that provided in Generalized Linear Models course.
Introduction to Bayesian Computing and Techniques
- Skill: Intermediate, Advanced
- Credit Options: CAP, CEU
Generalized Linear Models
- Skill: Intermediate, Advanced
- Credit Options: CAP, CEU
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Introduction to MCMC and Bayesian Regression via rstan
Additional Information
Homework
Homework in this course consists of short answer questions to test concepts and guided data analysis using software.
In addition to assigned readings, this course also has supplemental readings available online, end of course data modeling project, and example software codes.
Course Text
The required text for this course is “Applied Bayesian Modelling”, 2nd edition, by Peter Congdon.
Software
Selected R programs will be used in week 1, but the primary program used will be the freeware rstan, which can be downloaded from the R-Project.
Though the R programs used in week 1 will not require a high degree of familiarity with R, if you want to continue to use R with the entire course, you should have some prior experience and facility with it.
Supplemental Information
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Introduction to MCMC and Bayesian Regression via rstan