Scan statistic
= Scan statistic
{title2=$T=\max_{S\in\mathcal S}T_S$}
A scan statistic searches a family of candidate locations or subsets and reports the largest local <statistic>. Under a <null hypothesis>, a <union bound> converts a tail estimate for each candidate into a bound for the maximum; no <independence> between local <statistics> is required. Structured alternatives often permit a <chi-squared testing lower bound> using the overlap geometry of two candidates.