This is a two day workshop on some relatively advanced topics in Bayesian data analysis. On the first day, we cover Bayesian approaches to multilevel models including multilevel linear models and multilevel generalized linear models. For this, we will use the MCMCglmm R package and the Jags probabilistic programming language. On the second day, we cover Bayesian approaches to probabilistic mixture models and nonlinear regression. We also provide a more thorough introduction to the theoretical basis of Markov Chain Monte Carlo (MCMC) samplers. On the second day, we will primarily use Jags.

Day 1: Bayesian multilevel models

This workshop focuses on Bayesian data analysis using multilevel regression models. Given that Bayesian inference in almost all advanced probabilistic models is analytically intractable, the initial focus of this workshop will be on the theory and practice of Monte Carlo, and particularly Markov Chain Monte Carlo (MCMC), methods for drawing random samples from posterior probability distributions. Despite its relatively advanced nature, it is important to emphasize that MCMC methods are not a niche topic in Bayesian data analysis. They are at the heart of almost all modern applications of Bayesian data analysis, and they are what have allowed Bayesian methods to become so influential in modern statistics. In addition, this workshop will also focus heavily on the nature and practice of multilevel regression modeling. Multilevel models are becoming increasingly prevalent in data analysis in psychology and the social sciences. Inference in multilevel models presents major challenges for classical methods, while inference using Bayesian methods is always possible in principle. The practical activities in this workshop will largely focus on the use of the BUGS/JAGS macro language. This is an extremely powerful general tool for Bayesian data analysis as it allows for MCMC based inference in arbitrary probabilistic models. We will introduce BUGS/JAGS by way of relatively simple models, followed by in depth application to multilevel models.

• 9.00am Registration (including tea & coffee)
  
• 9:30am Introduction to probabilistic modelling with R, Jags and rjags
  
• 10:30am Introduction to multilevel modelling
  
• 11:00am Practical multilevel modeling in R and R-studio
  
• 12:30pm Lunch (Newton Arkwright cafe)
• 1:30pm Running multilevel models in JAGS
  
• 3:30pm Break (including tea & coffee)
  
• 3:45pm Advanced multilevel modelling with JAGS
  
• 5:00pm Discussion
  
• 5:30pm Close

Day 2: Latent variable and nonlinear models

This workshop focuses on Bayesian latent variable modeling, particularly using mixture models. Mixture models, also known as latent class models, model probability distributions as finite or infinite sums of simple component distributions. As such, mixture models provide a general means for modeling unique and arbitrarily complex probability distributions. They are also routinely used in practice, particularly in psychometrics. Bayesian approaches to mixture modeling rely heavily on Dirichlet prior distributions over finite numbers of mixture component, and Dirichlet process priors over infinitely many components. These Dirichlet process mixture models provide an elegant solution to the otherwise formidable challenge of inferring the correct number of components in mixture models. This workshop also focuses on Bayesian approaches to nonlinear regression modeling using Gaussian process models. Gaussian process regression represents a unifying approach to nonlinear regression, with many particular approaches to nonlinear regression - radial basis function, multilayer perceptrons, splines - being special cases of this general form.

Schedule

• 9.00am Registration (including tea & coffee)
  
• 9:30am Introduction to mixture modelling
  
• 10:30am Mixture modelling using JAGS
  
• 11:30am Dirichlet process mixture modelling
  
• 12:30pm Lunch (Newton Arkwright cafe)
• 1:30pm Introduction to nonlinear regression
  
• 2:30pm Nonlinear regression with basis functions
  
• 3:30pm Break (including tea & coffee)
  
• 4:00pm Gaussian process regression
  
• 5:00pm Discussion
  
• 5:30pm Close

GitHub resources

Further resources for this training course can be found on Github at mark-andrews/priorexposure.