The Quantile Snapshot Scan: Comparing Quantiles of Spatial Data from Two Snapshots in Time

We introduce the Quantile Snapshot Scan (Qsnap), a spatial scan algorithm which identifies spatial regions that differ the most between two snapshots in time. Qsnap is designed for spatial data with a numeric response and a vector of associated covariates for each spatial data point. Qsnap focuses on differences involving a specific quantile of the data distribution. A naive implementation of Qsnap is too computationally expensive for large datasets but our novel incremental update provides an order of magnitude speedup. We demonstrate Qsnap’s effectiveness over an extensive set of experiments on simulated data. In addition, we apply Qsnap to two real-world problems: discovering bird migration paths and identifying regions with dramatic changes in drought conditions.