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Bayesian Inference with R

( Duration: 3 Days )

Bayesian Inference with R training course teaches 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, delegates will learn the theoretical underpinnings of inference (with a focus on Bayesian statistics), along with applied examples of Bayesian approaches to statistical models.

By attending Bayesian Inference with R workshop, delegates will learn to:

  • 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)

  • 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.
  • 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.



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
  • JAGS
  • STAN

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