On the consistent and scalable detection of spatial patterns

TL;DR

This paper unifies spatial pattern detection methods, reveals inconsistencies in widely used techniques, and introduces scalable, robust tests suitable for large-scale spatial omics data analysis.

Contribution

It provides a unified framework for spatial pattern detection, identifies inconsistencies in existing methods, and proposes scalable corrections for large datasets.

Findings

Moran's I is inconsistent for spatial pattern detection.

The proposed test is scalable to millions of spatial locations.

The unified framework improves robustness and statistical validity.

Abstract

Detecting spatial patterns is fundamental to scientific discovery, yet current methods lack statistical consensus and face computational barriers when applied to large-scale spatial omics datasets. We unify major approaches through a single quadratic form and derive general consistency conditions. We reveal that several widely used methods, including Moran's I, are inconsistent, and propose scalable corrections. The resulting test enables robust pattern detection across millions of spatial locations and single-cell lineage-tracing datasets.