Approximation for the Distribution of Three-dimensional Discrete Scan Statistic

TL;DR

This paper develops approximation methods and error bounds for the distribution of three-dimensional discrete scan statistics, utilizing importance sampling to improve simulation accuracy, with applications to binomial and Poisson models.

Contribution

It introduces new approximation techniques and error bounds for 3D scan statistics, along with an importance sampling algorithm for sharper simulation bounds.

Findings

Provides accurate approximations with error bounds

Demonstrates effectiveness through simulation results

Offers comparisons with existing methods

Abstract

We consider the discrete three dimensional scan statistics. Viewed as the maximum of an 1-dependent stationary r.v.'s sequence, we provide approximations and error bounds for the probability distribution of the three dimensional scan statistics. Importance sampling algorithm is used to obtains sharp bounds for the simulation error. Simulation results and comparisons with other approximations are presented for the binomial and Poisson models.