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Bayesian Hierarchical Models

In this video in our Ecological Forecasting lecture series Mike Dietze introduces Bayesian hierarchical models as a way of capturing observable, but unexplained, variability in processes by allowing model parameters to vary probabilistically. Considering the simple case of modeling data from multiple observation units (sites, plots, lakes, etc.), the hierarchical approach is contrasted with the traditional alternatives of lumping unit-to-unit variability versus fitting different units independently. We also introduce the concepts or random versus fixed effects and discuss the impacts of partitioning different uncertainties on inferences and predictions. From a forecasting perspective, hierarchical models also provide a natural means of formally distinguishing differences in within-unit versus outside-of-sample predictive uncertainty. The lecture also includes example JAGS code for simple hierarchical models and explores a more detailed examples of using hierarchical models to improve allometric predictions of tree canopies, Coho salmon reproduction, and leaf photosynthesis.