Stan (https://mc-stan.org) is “a state-of-the-art platform for statistical modeling and high-performance statistical computation. Thousands of users rely on Stan for statistical modeling, data analysis, and prediction in the social, biological, and physical sciences, engineering, and business.” Stan is a powerful programming language for developing and fitting custom Bayesian statistical models. In this course, we provide a general introduction to the Stan language, and describe how to use it to develop and run Bayesian models. We begin by first covering the theory behind Stan, which covers Bayesian inference, Markov Chain Monte Carlo (MCMC) for sampling from probability distributions, and the efficient Hamiltonian Monte Carlo (HMC) method that Stan implements. Next, we learn how to write Stan models by creating simple Bayesian such as binomial models and models using normal distributions. In so doing, the basics of the Stan language will be apparent. Although Stan can be used with multiple different type of statistical programs (Python, Julia, Matlab, Stata), we will use Stan with R exclusively, specifically using the rstan or cmdstanr packages. Using thesepackages, we will can compile and sample from a HMC sampler for the Bayesian models we defined, plot and summarize the results, evaluate the models, etc. We then cover some widely used and practically useful models including linear regression, logistic regression, multilevel and mixed effects models. We will end by covering some more complex models, including probabilistic mixture models.
This course is aimed at anyone who is in interested in doing advanced Bayesian data analysis using Stan. Stan is a state of the art tool for advanced analysis across all academic scientific disciplines, engineering, and business, and other sectors.
Last Up-Dated – 21.01.2022
Duration – Approx. 15 hours
ECT’s – Equal to 1 ECT’s
Language – English
This course will be largely practical, hands-on, and workshop based. For each topic, there will first be some lecture style presentation, i.e., using slides or blackboard, to introduce and explain key concepts and theories. Then, we will cover how to perform the various statistical analyses using R. Any code that the instructor produces during these sessions will be uploaded to a publicly available GitHub site after each session. For the breaks between sessions, and between days, optional exercises will be provided. Solutions to these exercises and brief discussions of them will take place after each break.
Although not strictly required, using a large monitor or preferably even a second monitor will make the learning experience better, as you will be able to see my RStudio and your own RStudio simultaneously.
All the sessions will be video recorded, and made available immediately on a private video hosting website. Any materials, such as slides, data sets, etc., will be shared via GitHub.
We assume familiarity with inferential statistics concepts like hypothesis testing and statistical significance, and practical experience with linear regression, logistic regression, mixed effects models using R.
Some experience and familiarity with R is required. No prior experience with Stan itself is required.
A laptop computer with a working version of R or RStudio is required. R and RStudio are both available as free and open source software for PCs, Macs, and Linux computers. R may be downloaded by following the links here https://www.r-project.org/. RStudio may be downloaded by following the links here: https://www.rstudio.com/.
All the R packages that we will use in this course will be possible to download and install during the workshop itself as and when they are needed, and a full list of required packages will be made available to all attendees prior to the course.
A working webcam is desirable for enhanced interactivity during the live sessions, we encourage attendees to keep their cameras on during live zoom sessions.
Although not strictly required, using a large monitor or preferably even a second monitor will improve he learning experience
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Approx. 4 Hours
Topic 1: Hamiltonian Monte Carlo for Bayesian inference. We begin by describing Bayesian inference, whose objective is the calculation of a probability distribution over a high dimensional space, namely the posterior distribution. In general, this posterior distribution can not be described analytically, and so to summarize or make predictions from the posterior distribution, we must draw samples from it. For this, we can use Markov Chain Monte Carlo (MCMC) methods including the Metropolis sampler, sometimes known as random-walk Metropolis. Hamiltonian Monte Carlo (HMC), which Stan implements, is ultimately an efficient version of the Metropolis sampler that does not involve random walk behaviour. In this introductory section of the course, we will go through these major theoretical topics in sufficient detail to be able to understand how Stan works.
Topic 2: Univariate models. To learn the Stan language and how to use it to develop Bayesian models, we will start with simple models. In particular, we will look at binomial models and models involving univariate normal distributions. The models will allow us to explore many of the major features of the Stan language, including how to specify priors, in conceptually easy examples. Here, we will also learn how to use rstan and cmdstanr to compile the HMC sampler from the defined Stan model, and draw samples from it.
Approx. 4 Hours
Topic 2: Univariate models continued
Topic 3: Regression models. Having learned the basics of Stan using simple models, we now turn to more practically useful examples including linear regression, general linear models with categorical predictor variables, logistic regression, Poisson regression, etc. All of these examples involve the use of similar programming features and specifications, and so they are easily extensible to other regression models.
Approx. 4 Hours
Topic 4: Multilevel and mixed effects models. As an extension of the regression models that we consider in the previous topic, here we consider multilevel and mixed effects models. We primarily concentrate on linear mixed effects models, and consider the different ways to specify these models in Stan.
Topic 5: Because Stan is a programming language, it essentially gives us the means to create any bespoke or custom statistical model, and not just those that are widely used. In this final topic, we will cover some more complex cases to illustrate it power. In particular, we will cover probabilistic mixture models, which are a type of latent variable model.
Senior Lecturer, Psychology Department, Nottingham Trent University, England
Mark Andrews is a Senior Lecturer in the Psychology Department at Nottingham Trent University in Nottingham, England. Mark is a graduate of the National University of Ireland and obtained an MA and PhD from Cornell University in New York. Mark’s research focuses on developing and testing Bayesian models of human cognition, with particular focus on human language processing and human memory. Mark’s research also focuses on general Bayesian data analysis, particularly as applied to data from the social and behavioural sciences. Since 2015, he and his colleague Professor Thom Baguley have been funded by the UK’s ESRC funding body to provide intensive workshops on Bayesian data analysis for researchers in the social sciences.