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.

The course will take place online using Zoom. On each day, the live video broadcasts will occur during UK local time (GMT+0) at:
• 12pm-2pm
• 3pm-5pm
• 6pm-8pm

All sessions will be video recorded and made available to all attendees as soon as possible, hopefully soon after each 2hr session.

If some sessions are not at a convenient time due to different time zones, attendees are encouraged to join as many of the live broadcasts as possible. For example, attendees from North America may be able to join the live sessions from 3pm-5pm and 6pm-8pm, and then catch up with the 12pm-2pm recorded session once it is uploaded. By joining any live sessions that are possible will allow attendees to benefit from asking questions and having discussions, rather than just watching prerecorded sessions.

At the start of the first day, we will ensure that everyone is comfortable with how Zoom works, and we’ll discuss the procedure for asking questions and raising comments.

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.

Assumed quantitative knowledge

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.

Assumed computer background

Some experience and familiarity with R is required. No prior experience with Stan itself is required.

Equipment and software requirements

A 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. In addition to R and RStudio, some R packages, particularly rstan and cmdstanr, are required. Installing these packages will install Stan, which is a standalone program to R. Instructions on how to install R/RStudio and all required R packages will be provided before the course begins.

UNSURE ABOUT SUITABLILITY THEN PLEASE ASK oliverhooker@prstatistics.com

Wednesday 2nd – Classes from 12:00 to 20:00

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.

Thursday 3rd – Classes from 12:00 to 20:00

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.

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.