Despite the promise of big data, inferences are often limited not by the size of data but rather by its systematic structure. Only by carefully modeling this structure can we take fully advantage of the data -- big data must be complemented with big models and the algorithms that can fit them. Stan is a platform for facilitating this modeling, providing an expressive modeling language for specifying bespoke models and implementing state-of-the-art algorithms to draw subsequent Bayesian inferences.
These modules present a modern perspective on Bayesian modeling, beginning with a principled Bayesian workflow and then progressing to in depth reviews of popular modeling techniques. The course will emphasize interactive exercises run through RStan, the R interface to Stan, and PyStan, the Python interface to Stan.
The course is aimed at current Stan users and will assume familiarity with the basics of calculus, linear algebra, probability theory, probabilistic modeling and statistical inference, and Stan.
Attendees are strongly encouraged to review
Conditional Probability Theory:
(See also https://betanalpha.github.io/assets/case_studies/conditional_probability.pdf)
Probability Theory on Product Spaces
Sampling and The Monte Carlo Method
Common Families of Probability Density Functions
Markov chain Monte Carlo
(See also https://betanalpha.github.io/assets/case_studies/markov_chain_monte_carlo_basics.html)
Introduction to Stan
In order to participate in the exercises attendees must have a computer with RStan 2.19 and at least R 4.0 or PyStan 2.19 and at least Python 3.7 installed. Please verify that you can run the 8 schools model as discussed in https://github.com/stan-dev/rstan/wiki/RStan-Getting-Started or https://pystan2.readthedocs.io/en/latest/getting_started.html and report any installation issues at http://discourse.mc-stan.org as early as possible. While the exercises cannot be run directly with other Stan interfaces such as CmdStanR, CmdStanPy, and PyStan3 they are relatively straightforward to translate.
If you are interested in a more introductory presentation Jumping Rivers will also be hosting a one-day course that introduces Bayesian inference on Februrary 20th and a three-day course that introduces Bayesian inference with Stan from February 20th to February 22nd.
Each module except for the first consists of a live lecture followed by exercises for attendees to complete individually before a final live review session. The modules are offered in parallel morning and afternoon sessions for scheduling flexibility; the morning and afternoon sessions of each module cover the same material and attendees are recommended to attend only one session!
The lecture and review will take place on Whereby which does not require any registration from attendees. Both will be recorded and the recording will be made available to course attendees soon after each session concludes. By participating you consent to having any video and audio you transmit recorded and shared with the rest of the course attendees. Not sharing your video and audio will not prevent you from viewing the sessions or asking questions through the interactive chat.
In between the lecture and review session attendees will be able to discuss the lecture and the exercises with each other on Discord. You should be able to access the course-specific Discord servers without any registration.
The nine course modules are organized into three suites, each consisting of three modules dedicated to a particular topic. Suite 1 focuses on general topics in Bayesian modeling, Suite 2 analyzes regression from this modeling perspective, and Suite 3 develops modeling techniques for quantifying heterogeneity. Because each module within a suite builds on top of the previous ones I encourage attending them in order to for the most benefit.
The Modeling Suite
Module 1: Probabilistic and Generative Modeling
Module 1 discusses probabilistic modeling with an emphasis on generative models that capture the particular details of an assumed data generating process. The first lecture reviews the conceptual foundations of probabilistic modeling and statistical inference while the second lecture focuses on techniques for developing bespoke generative models.
First Lecture: Mon Feb 6 10:00 EST - 12:00 EST
Second Lecture: Thursday Feb 9 10:00 EST - 12:00 EST
First Lecture: Mon Feb 6 15:00 EST - 17:00 EST
Second Lecture: Thursday Feb 9 15:00 EST - 17:00 EST
Module 2: Identifiability and Degeneracy
The second module concerns uncertainty, introducing the quantitative concept of the identifiability of probabilistic models and the more qualitative, but more practically relevant, concept of degeneracy of statistical inferences. We will review strategies for not only identifying and investigating degenerate behavior but also managing the pathological consequences of that behavior.
Lecture: Mon Feb 13 10:00 EST - 12:00 EST
Review Session: Thursday Feb 16 10:00 EST - 11:30 EST
Lecture: Mon Feb 13 15:00 EST - 17:00 EST
Review Session: Thursday Feb 16 15:00 EST - 16:30 EST
Module 3: Principled Bayesian Model Development Workflow
In this module we review a workflow that guides the development of Bayesian models suited to the particular details of a given application. The workflow integrates the development of prior model elicitation, experimental design, model critique and model updating.
Lecture: Mon Feb 20 10:00 EST - 12:00 EST
Review Session: Thursday Feb 23 10:00 EST - 11:30 EST
Lecture: Mon Feb 20 15:00 EST - 17:00 EST
Review Session: Thursday Feb 23 15:00 EST - 16:30 EST
The Regression Suite
Module 4: Variate Covariate Modeling
This module considers regression from a Bayesian modeling perspective, investigating the crucial but often overlooked assumptions inherent to these techniques. The discussion will place a particular focus on the inferential consequences of confouding.
Lecture: Mon Mar 6 10:00 EST - 12:00 EST
Review Session: Thursday Mar 9 10:00 EST - 11:30 EST
Lecture: Mon Mar 6 15:00 EST - 17:00 EST
Review Session: Thursday Mar 9 15:00 EST - 16:30 EST
Module 5: Taylor Modeling
Module 5 introduces linear regression as a local approximation of more general regression analyses. The theory of Taylor approximations offers interpretability and guidance for how these linear models, and the heuristics that often accompany them, can be robustly applied in practice.
Lecture: Mon Mar 13 10:00 EST - 12:00 EDT
Review Session: Thursday Mar 16 10:00 EDT - 11:30 EDT
Lecture: Mon Mar 13 15:00 EST - 17:00 EDT
Review Session: Thursday Mar 16 15:00 EDT - 16:30 EDT
Module 6: General Taylor Modeling
In this module we will combine Taylor approximation with unconstraining transformations to build robust models for regression analyses with constraints. We will consider the special cases of exponential and logistic regression, including the development of principled prior models for theses analyses.
Lecture: Mon Mar 20 10:00 EST - 12:00 EDT
Review Session: Thursday Mar 23 10:00 EDT - 11:30 EDT
Lecture: Mon Mar 20 15:00 EST - 17:00 EDT
Review Session: Thursday Mar 23 15:00 EDT - 16:30 EDT
The Heterogeneity Suite
Module 7: Hierarchical Modeling
Module 7 introduces exchangeability and hierarchical models for heterogeneous data generating processes. We will place a strong focus on the inherent identifiability issues and their computational consequences, as well as strategies for moderating this issues.
Lecture: Mon Apr 3 10:00 EST - 12:00 EDT
Review Session: Thursday Apr 6 10:00 EDT - 11:30 EDT
Lecture: Mon Apr 3 15:00 EST - 17:00 EDT
Review Session: Thursday Apr 6 15:00 EDT - 16:30 EDT
Module 8: Factor Modeling
This module introduces conditional exchangeability, marginal exchangeability, and observed factor modeling (also known as multilevel or random effects modeling) with a focus on robust and efficient implementations.
Lecture: Mon Apr 10 10:00 EST - 12:00 EDT
Review Session: Thursday Apr 13 10:00 EDT - 11:30 EDT
Lecture: Mon Apr 10 15:00 EST - 17:00 EDT
Review Session: Thursday Apr 13 15:00 EDT - 16:30 EDT
Module 9: Sparsity Modeling
The final module reviews the concept of sparsity in Bayesian inference and hierarchical modeling techniques that can encourage sparse inferences of heterogeneous behavior.
Lecture: Mon Apr 17 10:00 EDT - 12:00 EDT
Review Session: Thursday Apr 20 10:00 EDT - 11:30 EDT
Lecture: Mon Apr 17 15:00 EDT - 17:00 EDT
Review Session: Thursday Apr 20 15:00 EDT - 16:30 EDT
Invoices and Certificates
Official invoices and certificates of completion will be available upon request.
Cancellations will be considered only in the event of emergencies. Those not able to attend the modules due to unexpected scheduling conflicts will be able to follow along with the recordings and Discord discussion groups. If you have any questions then don't hesitate to contact me.
If you are interested in purchasing more than 12 tickets then contact me about group discounts.
Unfortunately at this time I am unable to accommodate general academic discounts, but depending on availability I may be able to accommodate a few discounted tickets with priority given to black, indigenous people of color in high-income countries or those from low and middle-income countries. If you are interesting in inquiring about these opportunities then don't hesitate to contact me.
“We had a brilliant 3-day course at trivago with Michael Betancourt! The first day was filled with a very strong theoretical foundation for statistical modelling/decision making, followed by a crash course on MCMC and finished off with practical examples on how to diagnose healthy model fitting. In the 2nd and 3rd days we learned about many different types of hierarchical/multi-level models and spent most of the time practicing how to actually create and fit these models in Stan.
Michael is both a very engaging teacher, a very knowledgeable statistical modeller and, of course, a Stan master. This course has opened up new ways for us at trivago to gain better insights from our data through Stan models that fit our needs.”
-Data Scientists in the Automated Bidding Team, trivago
“The 1-day training course provided a great introduction to Bayesian models and their implementation in the Stan language. The practical focus really helped jumpstart our transition to Bayesian methods, and the slides, recorded lecture, and exercises also provide a great resource for new group members.”
-Stanley Lazic, Associate Director in Statistics and Machine Learning, AstraZeneca
“Stan is the cream of the crop platform for doing Bayesian analysis and is particularly appealing because of its open source nature. The programming language and algorithms are well designed and thought out. With that said, Stan has a very steep learning curve requiring lots of hours to get up to speed on your own. I have been to two training courses taught by Dr. Michael Betancourt and took an opportunity to have some consulting time. These sessions have proven invaluable to improve my use of Stan, increased my learning and usage rate, and informed me how to diagnose and detect issues that will inevitable will arise.”
-Robert Johnson, Corporate R&D, Procter & Gamble
“The workshop at MIT led by Michael Betancourt was a fun and very useful introduction to Stan. Mike worked with us to customize the lectures to our interests, he presented the material in an engaging and accessible way, and the physicists who attended, many of whom had never used Stan before, left with the resources to begin developing our own analyses. Mike’s background in physics makes him an especially effective teacher for scientists. The coding exercises were thoughtfully developed to progress in complexity and were well-integrated into the course; having such useful exercises was critical for participants to successfully internalize the concepts presented in the lectures.”
-Elizabeth Worcester, Associate Physicist, Department of Physics, Brookhaven National Laboratory