Bayesian hierarchical modeling of mucosal immune responses and growth efficiency in young animals: Demonstrating the superiority of data-dependent empirical priors.

The transition from milk to solid food during the weaning period exposes young animals to significant dietary and environmental stressors, which can profoundly affect mucosal immune responses and overall growth efficiency. This paper introduces a novel Bayesian hierarchical model to comprehensively assess the complex interactions between diet, environmental factors, intestinal microbiota, and immune markers in young animals' small intestines. The model integrates data at both individual and group levels, providing a robust framework to understand how these stressors influence immune responses and growth outcomes. This hierarchical Bayesian approach captures individual variability and group-level effects by employing sophisticated interaction terms and data-dependent empirical priors, offering high-resolution uncertainty quantification. The model's novelty lies in its ability to synthesize multiple sources of variability, offering insights that are not achievable through traditional statistical models.