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