Three-phase hierarchical model-based and hybrid inference

Global commitments to mitigating climate change and halting biodiversity loss require reliable information about Earth's ecosystems. Increasingly, such information is obtained from multiple sources of remotely sensed data combined with data acquired in the field. This new wealth of data poses challenges regarding the combination of different data sources to derive the required information and assess uncertainties. In this article, we show how predictors and their variances can be derived when hierarchically nested models are applied. Previous studies have developed methods for cases involving two modeling steps, such as biomass prediction relying on tree-level allometric models and models linking plot-level field data with remotely sensed data. This study extends the analysis to cases involving three modeling steps to cover new important applications. The additional step might involve an intermediate model, linking field and remotely sensed data available from a small sample, for making predictions that are subsequently used for training a final prediction model based on remotely sensed data: • In cases where the data in the final step are available wall-to-wall, we denote the approach three-phase hierarchical model-based inference (3pHMB), • In cases where the data in the final step are available as a probability sample, we denote the approach three-phase hierarchical hybrid inference (3pHHY).