Being Bayesian in the 2020s: opportunities and challenges in the practice of modern applied Bayesian statistics

Bayesian data analysis is now an established part of the lexicon in contemporary applied statistics and machine learning. There is now a wealth of practical know-how to complement the continued development and increasing access to Bayesian models, algorithms and software. There is also a weighty body of published case studies that testify to the successful implementation and associated benefits of the Bayesian paradigm in practice. However, as with all fields of knowledge, the task is unfinished: each success begets further opportunities and challenges, which in turn drive new directions for innovation in research and practice. In this paper, we identify six such directions that, among many others, are driving the evolution of applied Bayesian modelling in this decade. For each of these, we provide a brief overview of the issue and a case study that outlines our experience in practice.

The first direction focuses on intelligent data collection: instead of collecting and analysing all possible data, or alternatively relying on traditional static experimental or survey designs, can we devise efficient, cost-effective approaches to collecting those data that will be most informative for the inferential purpose? In §2, authors Buchhorn and McGree focus on the opportunity to address this issue through Bayesian optimal experimental design. While there is an emerging literature on this approach in the context of clinical trials, they extend this attention to sampling designs for complex ecosystems. Furthermore, they address the challenge of exact implementation of the derived design in practice by introducing sampling windows in the optimal design. The new methodology and computational solution are illustrated in a case study of monitoring coral reefs.

Following from consideration of data collection, the second direction considered in this paper focuses on opportunities and challenges afforded through the emergence of new data sources. In §3, authors Price, Santos-Fernández and Vercelloni focus on two such sources: quantitative information elicited from subjects in virtual reality (VR) settings, and data provided by citizen scientists. Bayesian approaches to modelling and analysing these data can help to increase trust in these data and facilitate their inclusion in mainstream analyses. Some methods for achieving this are set in the context of two case studies based in the Antarctic and the Australian Great Barrier Reef.