Chen, Jihong; Huo, Xiaoming Distribution of the length of the longest significance run on a Bernoulli net and its applications. (English) Zbl 1118.62308 J. Am. Stat. Assoc. 101, No. 473, 321-331 (2006). Summary: We consider the length of the longest significance run in a (two-dimensional) Bernoulli net and derive its asymptotic limit distribution. Our results can be considered as generalizations of known theorems in significance runs. We give three types of theoretical results: (1) reliability-style lower and upper bounds, (2) Erdös-Rényi 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. Cited in 4 Documents MSC: 62E20 Asymptotic distribution theory in statistics 90C39 Dynamic programming 65C60 Computational problems in statistics (MSC2010) PDFBibTeX XMLCite \textit{J. Chen} and \textit{X. Huo}, J. Am. Stat. Assoc. 101, No. 473, 321--331 (2006; Zbl 1118.62308) Full Text: DOI