Spatially constrained clustering and upper level set scan hotspot detection in surveillance geoinformatics

We discuss upper level set (ULS) scan as a type of spatially constrained clustering in relation to two ways of imposing the spatial constraint, retrospectively versus progressively. We show that ULS scan produces the same results both ways; whereas two popular clustering techniques, single-linkage and K-means, can yield different results when spatial constraints are imposed retrospectively versus progressively. The ULS scan approach examines spatially connected components of a tessellation as a threshold is moved from the highest level (value) in the data to the lowest level. When the variable of interest on the tessellation is a rate of incidence, then a significance test is available based on binomial or Poisson null models and Monte Carlo techniques. This is a common context for detecting hotspots of diseases in epidemiological work. We also discuss an approach for extending the univariate methodology to accommodate multivariate contexts. Received: September 2005 / Revised: February 2006 This material is based upon work supported by (i) the National Science Foundation under Grant No. 0307010, (ii) the United States Environmental Protection Agency under Grant No. CR-83059301 and (iii) the Pennsylvania Department of Health using Tobacco Settlement Funds under Grant No. ME 01324. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the agencies.     

Ranked set sampling: an annotated bibliography

The paper provides an up-to-date annotated bibliography of the literature on ranked set sampling. The bibliography includes all pertinent papers known to the authors, and is intended to cover applications as well as theoretical developments. The annotations are arranged in chronological order and are intended to be sufficiently complete and detailed that a reading from beginning to end would provide a statistically mature reader with a state-of-the-art survey of ranked set sampling, including historical development, current status, and future research directions and applications. A final section of the paper gives a listing of all annotated papers, arranged in alphabetical order by author.This paper was prepared with partial support from the United States Environmental Protection Agency under a Cooperative Agreement Number CR-821531. The contents have not been subject to Agency review and therefore do not necessarily reflect the views or policies of the Agency and no official endorsement should be inferred.     

Statistical Estimation and Model Selection of Species-Accumulation Functions

Abstract:  Soberón and Llorente (1993) proposed pure-birth stochastic processes as theoretical models for species-accumulation curves, and these processes have frequently been used to describe the progress of biological inventories. We describe, in algorithmic form, an alternative statistical analysis based on a likelihood approach ( Díaz-Francés & Gorostiza 2002 ) that provides mathematical rigor to the ideas in Soberón and Llorente (1993) and improves the estimation of the models by incorporating the facts that the variance of the error is not constant and that the observations are correlated. Additionally, we used the likelihood ratios between candidate models as an objective procedure for model selection, allowing comparison between the goodness of fit of various models. The software for these statistical methods can now be downloaded off the Internet. We used two examples of butterfly data sets to illustrate the use of the methods and the software.     

Statistical evaluation of the attainment of interim cleanup standards at hazardous waste sites

Cleanup standards at hazardous waste sites include (i) numeric standards (often risk-based), (ii) background standards in which the remediated site is compared with data from a supposedly clean region, and (iii) interim standards in which the remediated site is compared with preremediation data from the same site. The latter are especially appropriate for verifying progress when an innovative, but unproven, technology is used for remediation. Standards of type (i) require one-sample statistical tests, while those of type (ii) and type (iii) call for two-sample tests. This paper considers two-sample tests with an emphasis upon the type (iii) scenario. Both parametric (likelihood ratio) and nonparametric (linear rank) protocols are examined. The methods are illustrated with preremediation data from a site on the National Priorities List. The results indicate that nonparametric procedures can be quite competitive (in terms of power) with distributional modelling provided a near optimal rank test is selected. Suggestions are given for identifying such rank tests. The results also confirm the importance of sound baseline sampling; no amount of post-remediation sampling can overcome baseline deficiencies.This paper has been prepared with partial support from the United States Environmental Protection Agency under a Cooperative Agreement Number CR-815273. The contents have not been subject to Agency review and therefore do not necessarily reflect the views or policies of the Agency and no official endorsement should be inferred.     

Multiscale advanced raster map analysis system: Definition, design and development

This paper brings together a multidisciplinary initiative to develop advanced statistical and computational techniques for analyzing, assessing, and extracting information from raster maps. This information will provide a rigorous foundation to address a wide range of applications including disease mapping, emerging infectious diseases, landscape ecological assessment, land cover trends and change detection, watershed assessment, and map accuracy assessment. It will develop an advanced map analysis system that integrates these techniques with an advanced visualization toolbox, and use the system to conduct large case studies using rich sets of raster data, primarily from remotely sensed imagery. As a result, it will be possible to study and evaluate raster maps of societal, ecological, and environmental variables to facilitate quantitative characterization and comparative analysis of geospatial trends, patterns, and phenomena. In addition to environmental and ecological studies, these techniques and tools can be used for policy decisions at national, state, and local levels, crisis management, and protection of infrastructure. Geospatial data form the foundation of an information-based society. Remote sensing has been a vastly under-utilized resource involving a multi-million dollar investment at the national levels. Even when utilized, the credibility has been at stake, largely because of lack of tools that can assess, visualize, and communicate accuracy and reliability in timely manner and at desired confidence levels. Consider an imminent 21st century scenario: What message does a multi-categorical map have about the large landscape it represents? And at what scale, and at what level of detail? Does the spatial pattern of the map reveal any societal, ecological, environmental condition of the landscape? And therefore can it be an indicator of change? How do you automate the assessment of the spatial structure and behavior of change to discover critical areas, hot spots, and their corridors? Is the map accurate? How accurate is it? How do you assess the accuracy of the map? How do we evaluate a temporal change map for change detection? What are the implications of the kind and amount of change and accuracy on what matters, whether climate change, carbon emission, water resources, urban sprawl, biodiversity, indicator species, human health, or early warning? And with what confidence? The proposed research initiative is expected to find answers to these questions and a few more that involve multi-categorical raster maps based on remote sensing and other geospatial data. It includes the development of techniques for map modeling and analysis using Markov Random Fields, geospatial statistics, accuracy assessment and change detection, upper echelons of surfaces, advanced computational techniques for geospatial data mining, and advanced visualization techniques.     

Statistical selection of perimeter-area models for patch mosaics in multiscale landscape analysis

This paper presents a statistical method for detecting distinct scales of pattern for mosaics of irregular patches, by means of perimeter–area relationships. Krummel et al. (1987) were the first to develop a method for detecting different scaling domains in a landscape of irregular patches, but this method requires investigator judgment and is not completely satisfying. Grossi et al. (2001) suggested a modification of Krummel's method in order to detect objectively the change points between different scaling domains. Their procedure is based on the selection of the best piecewise linear regression model using a set of statistical tests. Even though the change points were estimated, the null distributions used for testing purposes were those appropriate for known change points. The present paper investigates the effect that estimating the change points has on the underlying distribution theory. The procedure we suggest is based on the selection of the best piecewise linear regression model using a likelihood ratio (LR) test. Each segment of the piecewise linear model corresponds to a fractal domain. Breakpoints between different segments are unknown, so the piecewise linear models are non-linear. In this case, the frequency distribution of the LR statistic cannot be approximated by a chi-squared distribution. Instead, Monte Carlo simulation is used to obtain an empirical null distribution of the LR statistic. The suggested method is applied to three patch types (CORINE biotopes) located in the Val Baganza watershed of Italy.     

Monitoring of Daily Integrated Exposure of Outdoor Workers to Respirable Particulate Matter in an Urban Region of India

It is more and more recognised that an estimation of the exposure of the population to air pollutants is more relevant than the ambient air quality, since it gives a better indication of health risk. Outdoor workers in an urban region are generally of low income status and are exposed to higher levels of both indoor and outdoor air pollution. Hence respondents from this population subgroup have been selected for this study. Outdoor workers are divided into two categories, viz. traffic constables and casual outdoor workers like watchmen, roadside shopkeepers etc. Most of the respondents are from the lower income group. Each respondent is monitored for a continuous 48-hour period. The sampling frequency is once a week.The study region is situated in the north-west part of the Greater Mumbai Municipal Corporation. It can be classified as industrial cum residential area. The daily integrated exposure of the outdoor workers consists of two major micro-environments, viz. occupational and indoor residential.A personal air sampler was used along with a cyclone to measure levels of Respirable Particulate Matter (RPM). The cyclone has a 50% removal efficiency for particle diameter of 5 m. Paired samples of PM10 (ambient) and RPM (personal) were collected to establish the correlation between them. The average 24-hour integrated exposure to RPM was 322 g/m3 and exceeded the corresponding PM10 level observed at the nearest Ambient Air Quality Monitoring Station by a factor of 2.25. The 90% confidence interval for this exposure is 283–368 g/m3. This study clearly demonstrates that the daily integrated exposure and therefore the health risk of outdoor workers in an urban area is significantly more serious than that indicated by ambient air quality data.     

A composite receptor and dispersion model approach for estimation of effective emission factors for vehicles

It is difficult to estimate vehicular emission factors at traffic junctions for use in dispersion modelling studies. Firstly, because the vehicles are in various modes of operation and secondly, it is difficult to delineate the effects of other contributing sources, mainly the effects of road dust and deposited constituents, which are very prominent at traffic junctions in India. Factor analysis-multiple regression (FA-MR), a receptor modelling technique has been used in this study for apportioning the contributing sources. The measurement data consist of one year's temporal variation of suspended particulate matter (SPM), analysed for its trace metal constituents, and two gaseous components NO₂ and SO₂ at two traffic junctions in Mumbai (India). FA-MR apportioned 40% of the observed SPM to road dust and 15% to vehicular sources. Of the total Pb observed in the SPM, FA-MR apportioned 60% to vehicular sources and 20% to road dust. The field-observed vehicular counts, meteorological parameters and road geometry were used in California line source dispersion model to estimate the effective vehicular emission factor for Pb at one traffic junction. This derived emission factor was used to predict the Pb concentration at second (independent observation) traffic junction. The result was found to be more satisfactory than using default emission factors obtained from literature. Similarly, effective vehicular emission factor for NO₂ was also evaluated for one site and tested for predicting concentrations at the other site.     

Sensitivity of normal theory methods to model misspecification in the calculation of upper confidence limits on the risk function for continuous responses

Normal theory procedures for calculating upper confidence limits (UCL) on the risk function for continuous responses work well when the data come from a normal distribution. However, if the data come from an alternative distribution, the application of the normal theory procedures may lead serious over- or under-coverage depending upon the alternative distribution. In this paper we conduct simulation studies to investigate the sensitivity of three normal theory UCL procedures to departures from normality. Data from several gamma, reciprocal gamma, and lognormal distributions are considered. The normal theory procedures are applied to both the raw data and the log-transformed data.