Distribution of the length of the longest significance run on a Bernoulli net and its applications

• 成果类型: Article
• 署名作者: Chen, JH; Huo, XM
• 署名单位: University System of Georgia; Georgia Institute of Technology
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1198/016214505000000574
• 发表日期: 2006
• 页码: 321-331
• 关键词: Random variables; approximation; probabilities; sequence; LAW

摘要

We consider the length of the longest significance run in a (two-dimensional) Bernoulli net and derive its asymptotic limit distribution. Our theoretical results: (1) reliabilityresults can be considered as generalizations of known theorems in significance runs. We give three types of t style lower and upper bounds, (2) Erdos-Renyi law, and (3) the asymptotic limit distribution. To understand the rate of convergence to the asymptotic distributions, we carry out numerical simulations. The convergence rates in a variety of situations are presented. To understand the relation between the length of the longest significance run(s) and the success probability p. we propose a dynamic programming algorithm to implement simultaneous simulations. Insights from numerical studies are important for choosing the values of design parameters in a particular application, which motivates this article. The distribution of the length of the longest significance run in a Bernoulli net is critical in applying a multiscale methodology in image detection and computational vision. Approximation strategies to some critical quantities are discussed.