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Bayesian calibration of simulation models: A tutorial and an Australian smoking behaviour model

Simulation models of epidemiological, biological, ecological, and environmental processes are increasingly being calibrated using Bayesian statistics. The Bayesian approach provides simple rules to synthesise multiple data sources and to calculate uncertainty in model output due to uncertainty in the calibration data. As the number of tutorials and studies published grow, the solutions to common difficulties in Bayesian calibration across these fields have become more apparent, and a step-by-step process for successful calibration across all these fields is emerging. We provide a statement of the key steps in a Bayesian calibration, and we outline analyses and approaches to each step that have emerged from one or more of these applied sciences. Thus we present a synthesis of Bayesian calibration methodologies that cut across a number of scientific disciplines. To demonstrate these steps and to provide further detail on the computations involved in Bayesian calibration, we calibrated a compartmental model of tobacco smoking behaviour in Australia. We found that the proportion of a birth cohort estimated to take up smoking before they reach age 20 years in 2016 was at its lowest value since the early 20th century, and that quit rates were at their highest. As a novel outcome, we quantified the rate that ex-smokers switched to reporting as a 'never smoker' when surveyed later in life; a phenomenon that, to our knowledge, has never been quantified using cross-sectional survey data.