An Efficient Quantile Spatial Scan Statistic for Finding Unusual Regions in Continuous Spatial Data with Covariates

Abstract

Domains such as citizen science biodiversity monitoring and real estate sales are producing spatial data with a continuous response and a vector of covariates associated with each spatial data point. A common data analysis task involves finding unusual regions that differ from the surrounding area. Existing techniques compare regions according to the means of their distributions to measure unusualness. Comparing means is not only vulnerable to outliers, but it is also restrictive as an analyst may want to compare other parts of the probability distributions. For instance, an analyst interested in unusual areas for high-end homes would be more interested in the 90th percentile of home sale prices than in the mean. We introduce the Quantile Spatial Scan Statistic (QSSS), which finds unusual regions in spatial data by comparing quantiles of data distributions while accounting for covariates at each data point. We also develop an exact incremental update of the hypothesis test used by the QSSS, which results in a massive speedup over a naive implementation.