Calibrating the scan statistic with size-dependent critical values: heuristics, methodology and computation

TL;DR

This paper reviews methods for calibrating scan statistics with size-dependent critical values, enabling optimal detection of signals across various sizes without loss of power, and discusses algorithms for efficient computation.

Contribution

It introduces heuristics and methodologies for setting size-dependent critical values in scan statistics, improving detection power across signal sizes.

Findings

Size-dependent critical values improve detection power for all signal sizes.

Fast algorithms enable efficient computation of scan statistics with size-dependent thresholds.

Application to multivariate settings broadens the method's applicability.

Abstract

It is known that the scan statistic with variable window size favors the detection of signals with small spatial extent and there is a corresponding loss of power for signals with large spatial extent. Recent results have shown that this loss is not inevitable: Using critical values that depend on the size of the window allows optimal detection for all signal sizes simultaneously, so there is no substantial price to pay for not knowing the correct window size and for scanning with a variable window size. This paper gives a review of the heuristics and methodology for such size-dependent critical values, their applications to various settings including the multivariate case, and recent results about fast algorithms for computing scan statistics.