Examining potential biases through prior predictive checks: Prior mis-specifications and their impact on Bayesian stock assessments

Bayesian stock assessment models are widely used to evaluate fish stock status and inform management decisions. The Bayesian approach enables the incorporation of prior information into assessment models, improving estimated precision and constraining over-parameterised models towards solutions that align with prior expectations. Understanding the interaction between joint priors across model parameters and the model likelihood is crucial for robust Bayesian inference, yet this aspect is seldom addressed in applied Bayesian stock assessments. Depending on the model, structural assumptions, and parameterisations, various prior mis-specification issues may emerge, leading to well-documented problems. In this study, we present two common prior mis-specifications using three stock assessment models of increasing complexity applied to South Atlantic albacore tuna data. The first mis-specification stems from an inconsistency between the prior and likelihood function, where the model structure implicitly modifies the prior to avoid negative biomass calculations. The second mis-specification involves uniform priors with constrained support on parameters like harvest rates or population scale, which, despite their intended non-informativeness, can be highly informative for derived quantities from the model. Simulations show that failing to address these issues in the likelihood function can result in misleading inference. We demonstrate that such issues can be mitigated by carefully encoding prior information with the help from prior predictive distributions of quantities directly linked to the likelihood function. To prevent potentially misinformed inference in Bayesian stock assessments, we recommend routinely conducting prior predictive checks to identify and correct unintended interactions between the likelihood and implicit information in joint priors.