A three day workshop introducing Bayesian data analysis. On the first day, we provide a general introduction to R. On the second day, we provide a general introduction to Bayesian data analysis and how it differs from the more familiar classical approaches to data analysis. On the third day, we delve more deeply into the theoretical and practical details of Bayesian inference, particularly focusing on Bayesian linear models.

The workshops will take place in room 424 of the Chaucer building (CH424) in Nottingham Trent University.

Day 1 (Wednesday, June 28, 2017)

The R programming language is now one of the most widely used tools for data-analysis worldwide. This is arguably due to a combination of its power and flexibility and the fact that is entirely based on free and open-source software. This workshop is a general introduction to R and how it can be used for general data-processing, statistical modelling and data-graphics. No previous experience with R, or with general programming, is necessary for this workshop.

Schedule

• 9:30am Introduction to R & RStudio
• 10:00am The fundamentals of R: Processing data, simple statistical tests, cheap and cheerful plots
• 12:30pm Lunch
• 1:30pm Linear models (linear regression, Anova, et al.) and generalized linear models (e.g. logistic regression, Poisson regression etc).
  
• 3:30pm Expert data wrangling with dplyr, tidyr and friends
• 4:30pm Visualizing data with ggplot
• 5:30pm Close

Day 2 (Thursday, June 29, 2017)

This workshop aims to be a general introduction to Bayesian data analysis and how it differs from the more familiar classical approaches to data analysis. We will start by providing a brief historical overview of statistical inference and introduce Bayes’s theorem. The fundamental concepts of Bayesian statistical inference will follow, contrasted with frequentist methods of inference. To provide a bridge between Bayesian and classical methods, we will describe likelihood function approaches to inference and introduce both the likelihood principle and the law of the likelihood as the general precepts of likelihood based inference. During this workshop, there will also be practical exercises, all involving the use of R, including using Bayes’s rule to calculate posterior probabilities and posterior distributions, choosing priors in probabilistic models and illustrating their role on the posterior distributions, calculating likelihood ratios and Bayes factors to compare evidence for different parameters in a probabilistic model, and calculating marginal likelihoods for comparing distinct probabilistic models.

Schedule

• 9.00am Registration (including tea & coffee)
• 9:30am Introduction and overview of workshop 1
• 10:00am Introduction to likelihood
• 11:30am Introduction to Bayesian inference
• 12:30pm Lunch (Newton Arkwright cafe)
• 1:30pm Bayesian data analysis in action
• 3:30pm Break (including tea & coffee)
• 3:45pm Bayes factors
• 5:00pm Discussion
• 5:30pm Close

Day 3 (Friday, June 30, 2017)

This workshop aims to provide a solid theoretical and practical foundation for real-world Bayesian data analysis in psychology and social sciences. It will focus primarily on the linear statistical models and so-called conjugate prior distributions. The reason for this focus is twofold. First, linear models — which include t tests, ANOVA, and linear regression models — are the core of the standard repertoire of statistical models with which our audience will be familiar. Studying the Bayesian counterparts of these approaches will therefore be a natural transition. Second, Bayesian inference in linear models with conjugate priors is analytically tractable, and this entails, amongst other things, that we can use relatively simple formulae to calculate the posterior distribution over the parameters and to make predictive inferences. This allows us to illustrate the general nature of Bayesian inference quickly and easily, postponing the computational and practical complications that arise as a consequence of performing Monte Carlo based numerical approaches to inference. In practical terms, this workshop will involve the use of the R statistical computing environment both to calculate posterior distributions in linear models and to graphically illustrate them. Indeed, graphically illustrating, for example, how the posterior distribution is a weighted average of the prior and likelihood functions and how the contribution of the likelihood function grows rapidly with increasing data, provides compelling intuitive insight into the nature of Bayesian inference.

Schedule

• 9.00am Registration (including tea & coffee)
• 9:30am Introduction and overview of workshop 2
• 10:00pm Bayesian inference in binomial models
• 11:30am Bayes and the German Tank Problem
• 12:30pm Lunch (Newton Arkwright cafe)
• 1:30pm Bayesian inference in Normal models
• 3:30pm Break (including tea & coffee)
• 3:45pm Bayesian inference in linear regression models
• 5:00pm Discussion
• 5:30pm Close