Multiresolution Decomposition of Areal Count Data

TL;DR

This paper extends multiresolution decomposition methods to irregular areal count data by integrating Besag--York--Mollié models, demonstrated through application to oral cavity cancer counts in Germany.

Contribution

It introduces a novel extension of multiresolution decomposition to irregular areal data using Besag--York--Mollié models, incorporating demographic information.

Findings

Feasibility demonstrated with oral cavity cancer data

Method effectively captures scale-dependent features in irregular data

Integration of demographic knowledge improves model accuracy

Abstract

Multiresolution decomposition is commonly understood as a procedure to capture scale-dependent features in random signals. Such methods were first established for image processing and typically rely on raster or regularly gridded data. In this article, we extend a particular multiresolution decomposition procedure to areal count data, i.e.~discrete irregularly gridded data. More specifically, we incorporate in a new model concept and distributions from the so-called Besag--York--Molli\'{e} model to include a priori demographical knowledge. These adaptions and subsequent changes in the computation schemes are carefully outlined below, whereas the main idea of the original multiresolution decomposition remains. Finally, we show the extension's feasibility by applying it to oral cavity cancer counts in Germany.