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Bayesian analyses offer a robust framework for integrating data from multiple sources to better inform population-level estimates of disease prevalence. This methodological approach is particularly suited to instances where data from observational studies is linked to administrative health records, with the capacity to advance our understanding of psychiatric disorders. The objective of our paper was to provide an introductory overview and tutorial on Bayesian analysis for primary observational studies in mental health research. We provided: (i) an overview of Bayesian statistics, (ii) the utility of Bayesian methods for psychiatric epidemiology, (iii) a tutorial example of a Bayesian approach to estimating the prevalence of mood and/or anxiety disorders in observational research, and (iv) suggestions for reporting Bayesian analyses in health research.