Confidence analysis of standard deviational ellipse and its extension into higher dimensional euclidean space

Bin Wang; Wenzhong Shi; Zelang Miao

doi:10.1371/journal.pone.0118537

Confidence analysis of standard deviational ellipse and its extension into higher dimensional euclidean space

PLoS One. 2015 Mar 13;10(3):e0118537. doi: 10.1371/journal.pone.0118537. eCollection 2015.

Authors

Bin Wang¹, Wenzhong Shi¹, Zelang Miao¹

Affiliation

¹ Department of Land Surveying and Geo-Informatics, The Hong Kong Polytechnic University, Kowloon, Hong Kong, China.

Abstract

Standard deviational ellipse (SDE) has long served as a versatile GIS tool for delineating the geographic distribution of concerned features. This paper firstly summarizes two existing models of calculating SDE, and then proposes a novel approach to constructing the same SDE based on spectral decomposition of the sample covariance, by which the SDE concept is naturally generalized into higher dimensional Euclidean space, named standard deviational hyper-ellipsoid (SDHE). Then, rigorous recursion formulas are derived for calculating the confidence levels of scaled SDHE with arbitrary magnification ratios in any dimensional space. Besides, an inexact-newton method based iterative algorithm is also proposed for solving the corresponding magnification ratio of a scaled SDHE when the confidence probability and space dimensionality are pre-specified. These results provide an efficient manner to supersede the traditional table lookup of tabulated chi-square distribution. Finally, synthetic data is employed to generate the 1-3 multiple SDEs and SDHEs. And exploratory analysis by means of SDEs and SDHEs are also conducted for measuring the spread concentrations of Hong Kong's H1N1 in 2009.

Publication types

Research Support, Non-U.S. Gov't

MeSH terms

Algorithms
Hong Kong / epidemiology
Humans
Influenza A Virus, H1N1 Subtype
Influenza, Human / epidemiology
Models, Theoretical*
Probability

Grants and funding

Mr. Bin Wang is the beneficiary of a doctoral grant from the AXA Research Fund. This study was supported by grants from the Ministry of Science and Technology of China (Project no. 2012BAJ15B04), the National Natural Science Foundation (Project no. 41331175), and National Administration of Surveying, Mapping and Geoinformation of China (Ling Jun Ren Cai). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.