An introduction to Bayesian geospatial analysis using a Bayesian multilevel model case study

Despite the rapidly growing interest in Bayesian inference, recent publications reveal common issues that suggest even experienced researchers across disciplines, including geospatial research, may not always follow the proper procedure in conducting Bayesian analysis and report results. This study aims to promote Bayesian inference and the best practice guidelines of Bayesian analysis, targeting beginners in the geospatial community. We selected the Bayesian multilevel model (BMLM) to demonstrate proper Bayesian analysis through a case study examining the effect of neighbourhood-level social deprivation on birthweight in Fulton County, Georgia, USA. We constructed both frequentist multilevel models (MLMs) and BMLMs, and these were two-level varying intercept models. Following the Avoid the Misuse of Bayesian Statistics (WAMBS) checklist, we illustrated the BMLM workflow and highlighted key steps in fitting, reporting, and interpreting BMLM. Our case study shows several advantages of the Bayesian approach over the frequentist method, including incorporating prior information, better handling of uncertainty, more intuitive interpretation, and greater transparency in reporting. However, some benefits, such as avoiding multiple comparisons and generating robust estimations, are challenging to explicitly illustrate. Other benefits such as handling small sample sizes and complex models cannot be showcased with our simple models. Notably, BMLM is more computationally intensive compared to MLMs. Adhering to established guidelines can enhance the quality, transparency, and reproducibility of Bayesian analysis, allowing us to fully harness the potential of Bayesian inference in advancing geospatial knowledge.