On selection and composition in small area and mapping problems

Maps in which small areas, such as districts, are represented by colours, shades or symbols with sizes determined by the values of estimates are regarded as an indispensable graphical output of analyses concerned with the geographical detail of economic, social, ecological and epidemiological phenomena. The distortion of the distribution of the district specific quantities in such maps, due to misrepresentation of the uncertainty about the estimated values, is discussed, and an alternative based on drawing so-called plausible maps is described. We highlight the pervasive and nonignorable nature of the selection process that identifies the quantity (target) to be estimated. A problem specific to disease mapping is what action, often one of a discrete set, to take in response to the results of an analysis. We argue that the costs (values) associated with correct and incorrect decisions should be integrated in the analysis and, when an analytical treatment is not feasible, plausible scenarios played out by simulations.