# A spatial dependence graph model for multivariate spatial hybrid processes

## TL;DR

This paper introduces a spatial dependence graph model for analyzing complex multivariate spatial data combining point and lattice processes, providing a unified framework for joint analysis and conditional independence assessment.

## Contribution

It develops a novel graph-based framework for multivariate hybrid spatial processes, integrating point and lattice data within a unified dependence model.

## Key findings

- Applied to crime and ambulance data in London, revealing dependence structures.
- Demonstrated the model's ability to handle mixed-type spatial data.
- Provided insights into spatial relationships between different incident types.

## Abstract

This paper is concerned with the joint analysis of multivariate mixed-type spatial data, where some components are point processes and some are of lattice-type by nature. After a survey of statistical methods for marked spatial point and lattice processes, the class of multivariate spatial hybrid processes is defined and embedded within the framework of spatial dependence graph models. In this model, the point and lattice sub-processes are identified with nodes of a graph whereas missing edges represent conditional independence among the components. This finally leads to a general framework for any type of spatial data in a multivariate setting. We demonstrate the application of our method in the analysis of a multivariate point-lattice pattern on crime and ambulance service call-out incidents recorded in London, where the points are the locations of different pre-classified crime events and the lattice components report different aggregated incident rates at ward level.