Bayesian Inference with R Training Overview
Accelebrate's Introduction to Bayesian Inference with R course teaches attendees the Bayesian approach to inference using the R language as the applied tool. After a quick review of importing and managing data with R as well as base R commands, students learn the theoretical underpinnings of inference (with a focus on Bayesian statistics), along with applied examples of Bayesian approaches to statistical models.
Location and Pricing
Accelebrate offers instructor-led enterprise training for groups of 3 or more online or at your site. Most Accelebrate classes can be flexibly scheduled for your group, including delivery in half-day segments across a week or set of weeks. To receive a customized proposal and price quote for private corporate training on-site or online, please contact us.
In addition, some courses are available as live, instructor-led training from one of our partners.
Objectives
- Understand how to import data to R for use in statistical modeling
- Review the frequentist approach to making inference on populations, using samples of data
- Non-comprehensive review of probability theory
- Understand maximum likelihood and restricted maximum likelihood
- Contrast frequentist approaches to inference with Bayesian approaches to inference
- Understand how prior distributions affect posterior distributions
- Review the difference between proper and improper priors
- Understand how to implement and explain an MCMC algorithm for obtaining empirical prior distributions
- Fit Bayesian modeling approaches to the general linear modeling framework
- Account for clustering and repeated events over time using Bayesian inference (generalized linear models)
- Make inference on functions of parameters
- Properly interpret Bayesian posterior density intervals
- Develop awareness of different modern software approaches to making Bayesian inference (with a focus on R)
Prerequisites
Students should have a basic background in R programming including importing and manipulating data, and an understanding of base R data structures such as vectors, matrices, lists, and dataframes. Students should also have a basic background in frequentist statistics to include hypothesis testing (p-values and null hypotheses), and statistical tests such as t-tests and chi-square tests. An understanding of the general linear modeling framework will be helpful, but is not required for this course.
Outline
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Introduction to Software Environment (R and RStudio)
Review of Base R
- Data import
- Creating new variables
- Basic summaries
- Plotting with R
Probability Theory and Notation with Applied Examples
Bayesian Models Versus Traditional Models
- The difference between a frequentist approach and a Bayesian approach
- Estimating cluster offsets
- Shrinkage
Estimating a Single Parameter
- Combing the prior and observed data
- The notion of a non-informative prior
- Summarizing the posterior
- Implementing MCMC algorithms
- Diagnosing MCMC chain output
- Checking posterior output
Applied Bayesian Regression Modelling: Normal Linear Regression
- Contrasting the Bayesian approach to linear regression
- Establishing model and data matrices
- Dimensionality reduction in the context of linear modeling
- Penalized models (shrinkage)
- Appropriate priors for beta and covariance parameters
- Diagnosing MCMC chain output
- Checking posterior output
- Non-linear terms
- Seasonal terms
- Extending this framework to clustered data
- Extensions to repeated measurements
Applied Bayesian Regression Modelling: Logistic Regression
- Extending Bayesian models to binary outcomes
- Accounting for over and under dispersion in a binomial model
- Extensions to clustered data
- Extensions to repeated measurements
Applied Bayesian Regression Modelling: Time to Event Models
- Extending Bayesian approaches to proportional hazards modeling
Review of Other Software Approaches to Performing Bayesian Inference
- INLA
- WINBUGS/OPENBUGS
- JAGS
- STAN
Conclusion
Training Materials
All R training attendees receive comprehensive courseware covering all topics in the course.
Software Requirements
- A recent release of R 4.x
- IDE or text editor of your choice (RStudio recommended)
