# An intuitive Bayesian spatial model for disease mapping that accounts for scaling

arXiv: https://arxiv.org/abs/1601.01180 · HTML: https://mlsanity.com/paper/1601.01180/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Jan 2016.

## Built on by (most cited first, 7 of 7)

- [PriorVAE: Encoding spatial priors with VAEs for small-area estimation](https://mlsanity.com/paper/2110.10422/) (2021)
- [PriorCVAE: scalable MCMC parameter inference with Bayesian deep generative modelling](https://mlsanity.com/paper/2304.04307/) (2023)
- [Deep learning and MCMC with aggVAE for shifting administrative boundaries: mapping malaria prevalence in Kenya](https://mlsanity.com/paper/2305.19779/) (2023)
- [Semi-Parametric Inference for Doubly Stochastic Spatial Point Processes: An Approximate Penalized Poisson Likelihood Approach](https://mlsanity.com/paper/2306.06756/) (2023)
- [Federated Learning for Non-factorizable Models using Deep Generative Prior Approximations](https://mlsanity.com/paper/2405.16055/) (2024)
- [Horseshoe Priors for Spatial Small Area Estimation: Regular Variation, Tail Robustness, and Deep Learning](https://mlsanity.com/paper/2606.30659/) (2026)
- [Planetary Geospatial Foundation Models: A New Paradigm for Global Public Health](https://mlsanity.com/paper/2610.05699/) (2026)

## Abstract (arXiv)

In recent years, disease mapping studies have become a routine application within geographical epidemiology and are typically analysed within a Bayesian hierarchical model formulation. A variety of model formulations for the latent level have been proposed but all come with inherent issues. In the classical BYM model, the spatially structured component cannot be seen independently from the unstructured component. This makes prior definitions for the hyperparameters of the two random effects challenging. There are alternative model formulations that address this confounding, however, the issue on how to choose interpretable hyperpriors is still unsolved. Here, we discuss a recently proposed parameterisation of the BYM model that leads to improved parameter control as the hyperparameters can be seen independently from each other. Furthermore, the need for a scaled spatial component is addressed, which facilitates assignment of interpretable hyperpriors and make these transferable between spatial applications with different graph structures. We provide implementation details for the new model formulation which preserve sparsity properties, and we investigate systematically the model performance and compare it to existing parameterisations. Through a simulation study, we show that the new model performs well, both showing good learning abilities and good shrinkage behaviour. In terms of model choice criteria, the proposed model performs at least equally well as existing parameterisations, but only the new formulation offers parameters that are interpretable and hyperpriors that have a clear meaning.