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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.

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## Review of Base R

• Data import
• Creating new variables
• Basic summaries
• Plotting with R
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## Bayesian Models Versus Traditional Models

• The difference between a frequentist approach and a Bayesian approach
• Estimating cluster offsets
• Shrinkage
5

## 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
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## 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
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## 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
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## Applied Bayesian Regression Modelling: Time to Event Models

• Extending Bayesian approaches to proportional hazards modeling
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## Review of Other Software Approaches to Performing Bayesian Inference

• INLA
• WINBUGS/OPENBUGS
• JAGS
• STAN