STRUCTURED, INTERACTIVE RESOURCES FOR TEACHING BAYESIAN INFERENCE
Gian Carlo Diluvi, Bruce Dunham, Nancy Heckman, Melissa Lee, and Rodolfo Lourenzutti
Department of Statistics, University of British Columbia, Canada
gian.diluvi@stat.ubc.ca
Most statistics undergraduate curricula provide only a brief introduction to Bayesian inference.
Furthermore, there is evidence that learners can fail to appreciate core concepts of the Bayesian
framework because of the focus on the mathematical formalism that is common in traditional instruction
of Bayesian inference. Guided exercises and interactive simulations are promising alternatives for
introducing Bayesian inference. However, these two types of resources have thus far been developed
separately, which may make them less effective. In this work, we bridge this gap by developing
interactive, structured resources in the form of web apps and accompanying activity sheets with guiding
exercises. We also incorporate student feedback via think-aloud sessions. This allows us to pinpoint
sources of confusion in students, e.g., problems constructing their priors.
INTRODUCTION
The Bayesian statistical framework has become a necessary element of a statistician's toolbox
due to its growing use in modern statistical problems (Albert, 2002; Gelman et al., 1995). Many
undergraduate curricula, however, have not kept up with the changes and typically only briefly
incorporate Bayesian inference as a small part of a course. For example, Dogucu and Hu (2022)
surveyed the statistics programs of the 152 highest ranked universities and colleges in the United States
and found that only 51 offered a Bayesian course. Of them, only four required students to take a
Bayesian course before graduating. Furthermore, instruction of Bayesian inference usually emphasizes
its mathematical underpinnings as opposed to focusing on core Bayesian concepts, something that has
been referred to as the legacy of mathematical thinking in statistics (Brown & Kass, 2009; Hoegh,
2020). These core concepts include, for example, the important role of the prior distribution in
incorporating expert knowledge into the statistical analysis and how the prior is combined with the
likelihood to update the practitioner's beliefs—encoded in the posterior distribution—about the
parameters (see the discussion by Johnson et al., 2020). In the mathematical thinking approach to
Bayesian inference, these key ideas remain hidden behind layers of algebra.
Previous work has focused on providing guidelines to teach introductory Bayesian courses
(Albert & Hu, 2020; Allenby & Rossi, 2008; Berry, 1997; Hoegh, 2020; Hu, 2020; Hu & Dogucu, 2022;
Johnson et al., 2020; Witmer, 2017). Most of these guidelines advocate for the use of both Bayesian-
specific introductory textbooks and interactive simulations with which students can engage. Bayesian
introductory textbooks (such as Albert & Hu, 2019; Berry, 1995; Johnson et al., 2022; and Kruschke,
2014) provide guided exercises tailored to help students achieve specific learning outcomes (e.g.,
understand that the posterior density is proportional to the prior density times the likelihood). On the
other hand, interactive simulations and web apps (e.g., Albert, 2020; Bárcena et al., 2019; O’Hagan,
1995) can completely hide the mathematical details in the backend, thereby allowing students to devote
more attention to core Bayesian concepts. Unlike textbooks, interactive resources are naturally suited
to showcase the dynamics of Bayesian inference, such as how the choice of prior distribution impacts
the posterior distribution.
So far, these two avenues have been developed separately: interactive simulations seldom
contain structure in the form of guided exercises, and textbooks are rarely accompanied by any
simulation. However, Lane and Peres (2006) found that interactive resources without structure are less
effective at aiding learning. Furthermore, these interactive simulations are usually developed without
any student input despite students being the intended end users. In this work, we bridge this gap by
developing open-source, online Shiny web apps (v1.7.1; Cheng et al., 2021) and accompanying activity
sheets with exercises that guide students towards achieving specific learning outcomes. Following the
methodology from Dunham et al. (2018), we also carried out think-aloud sessions where students
interacted with a web app (following the prompts of the activity sheet) and answered pre- and post-
interaction questionnaires. This allowed us to incorporate student feedback into the development of the
web apps and to pinpoint sources of confusion amongst students.
ICOTS11 (2022) Invited Paper - Refereed (DOI: 10.52041/iase.icots11.T10F2) Diluvi et al.
In S. A. Peters, L. Zapata-Cardona, F. Bonafini, & A. Fan (Eds.), Bridging the Gap: Empowering & Educating
Today’s Learners in Statistics. Proceedings of the 11th International Conference on Teaching Statistics (ICOTS11
2022), Rosario, Argentina. International Association for Statistical Education. iase-web.org ©2022 ISI/IASE