Parameter Estimation in Hierarchical Models: A Comparison of Bayesian and SGD-Adam Approaches on Biomass Data of Lutjanidae

Abstract

Hierarchical statistical models are widely used to analyse data with nested structures or repeated measurements, allowing variability across levels to be partitioned and providing more accurate parameter estimation than standard regression models. In the Bayesian framework, parameter estimation often uses Markov Chain Monte Carlo (MCMC), which accommodates complex structures and yields full posterior distributions. However, MCMC is computationally intensive, limiting scalability for large datasets. Recent advances in optimization methods, such as Hierarchical Stochastic Gradient Descent (HSGD) with Adaptive Moment Estimation (Adam), offer a faster and more efficient alternative for hierarchical models. This study applies Hierarchical Bayesian and HSGD-Adam approaches to fish biomass data of the family Lutjanidae from seven Marine Protected Areas (MPAs) in Raja Ampat, Indonesia. The model incorporates ecological predictors such as hard coral cover, distance to the nearest village and period of monitoring, with random effects for area of MPA. Comparison of predictive performance showed that the Bayesian model performed slightly better in RMSE, indicating its ability to capture extreme biomass variations, while SGD-Adam model achieved a lower MAE, reflecting greater stability in prediction. These findings demonstrate that advanced hierarchical modelling methods can enhance ecological data analysis and provide timely, data-driven insights for sustainable marine conservation policy.