Integrating Expert Knowledge and Recursive Bayesian Inference: A Framework for Spatial and Spatio-Temporal Data Challenges

Integrating heterogeneous data sources and expert knowledge is essential for overcoming data scarcity and enhancing estimation accuracy. Two main frameworks naturally arise to perform the integration of these multiple sources: sequential Bayesian inference and integrated models. The first one consists of updating posterior information in a sequential data analysis procedure, without the need to reanalyze previous data when new data become available. The second one consists of bringing together diverse sources of information in a joint inferential analysis through hierarchical Bayesian models. Within the context of the first framework, we propose a recursive inference method grounded in the methodological principles of INLA, designed to handle spatial and spatio-temporal problems, although its applicability is not limited to these cases, as the procedure is general in nature. Within the integrated models framework, we also present a comprehensive approach to address change of support issues that arise when combining heterogeneous information sources, developing a typology that classifies such changes as spatial, temporal, spatio-temporal, or categorical. Both frameworks can be combined, as there is neither a theoretical nor a practical incompatibility preventing their joint use. Finally, detailed examples are provided to illustrate clear and replicable procedures for combining heterogeneous data sources with change of support and recursive inference.