A Bayesian Solution to the Modifiable Areal Unit Problem

The Modifiable Areal Unit Problem (MAUP) prevails in the analysis of spatially aggregated data and influences pattern recognition. It describes the sensitivity of the measurement of spatial phenomena to the size (the scale problem) and the shape (the aggregation problem) of the mapping unit. Much attention has been recieved from fields as diverse as statistical physics, image processing, human geography, landscape ecology, and biodiversity conservation. Recently, in the field of spatial ecology, a Bayesian estimation was proposed to grasp how our description of species distribution (described by range size and spatial autocorrelation) changes with the size and the shape of grain. This Bayesian estimation (BYE), called the scaling pattern of occupancy, is derived from the comparison of pair approximation (in the spatial analysis of cellular automata) and join-count statistics (in the spatial autocorrelation analysis) and has been tested using various sources of data. This chapter explores how the MAUP can be described and potentially solved by the BYE. Specifically, the scale and the aggregation problems are analyzed using simulated data from an individual-based model. The BYE will thus help to finalize a comprehensive solution to the MAUP.