# A note on intrinsic Conditional Autoregressive models for disconnected graphs

## TL;DR

This paper discusses the definition, scaling, and implementation of intrinsic CAR models for disconnected graphs, providing practical guidelines and illustrating their application in disease mapping examples.

## Contribution

It offers new practical guidelines for defining and implementing intrinsic CAR models on disconnected graphs, addressing a gap in existing methodologies.

## Key findings

- Guidelines for defining intrinsic CAR models on disconnected graphs
- Implementation strategies demonstrated through disease mapping examples
- Enhanced understanding of model scaling and practical application

## Abstract

In this note we discuss (Gaussian) intrinsic conditional autoregressive (CAR) models for disconnected graphs, with the aim of providing practical guidelines for how these models should be defined, scaled and implemented. We show how these suggestions can be implemented in two examples on disease mapping.