Maps: A Statistical View

Abstract

Maps provide a data framework for the statistical analysis of georeferenced data observations. Since the middle of the twentieth century, the field of spatial statistics has evolved to address key inferential questions relating to spatially defined data, yet many central statistical properties do not translate to spatially indexed and spatially correlated data, and the development of statistical inference for mapped data remains an active area of research. Rather than review statistical techniques, we review the different ways the maps of georeferenced data can influence statistical analysis, focusing especially on maps as data visualization, maps as data structures, and maps as statistics themselves, i.e., summaries of underlying patterns with accompanying uncertainty. The categories provide connections to disparate literatures addressing spatial analysis including data visualization, cartography, spatial statistics, and geography. We find maps integrate spatial analysis from motivating questions, informing analytic methods, and providing context for results. Expected final online publication date for the Annual Review of Statistics and Its Application, Volume 11 is March 2024. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.