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.     

Spatial and space-time scan statistics to detect low rate clusters of sex ratio

Whether general environmental exposures to endocrine disrupting chemicals (including pesticides and dioxin) might induce decreased sex ratios (male/female ratio at birth) is discussed. To address this issue, the authors looked for a space-time clustering test which could detect local areas of significantly low risk, assuming a Bernoulli distribution. As a matter of fact, if the endocrine disruptor hypothesis holds true, and if the sex ratio is a sentinel health event indicative of new reproductive hazards ascribed to environmental factors, then in a given region, either a cluster of low male/female ratio among newborn babies would be expected in the vicinity of polluting municipal solid waste incinerators (MSWIs) (supporting the dioxin hypothesis), or local clusters would be expected in some rural areas where large amounts of pesticides are sprayed. Among cluster detection tests, the spatial scan statistic has been widely used in various applications to scan for areas with high rates, and rarely (if ever) with low rates. Therefore, the goal of this paper was to check the properties of the scan statistics under a given scenario (Bernoulli distribution, search for clusters with low rates) and to assess its added value in addressing the sex ratio issue. This study took place in the Franche-Comté region (France), mainly rural, comprising three main MSWIs, among which only one had high dioxin emissions level in the past. The study population consisted of 192,490 boys and 182,588 girls born during the 1975–1999 period. On the whole, the authors conclude that: (i) spatial and space-time scan statistics provide attractive features to address the sex ratio issue; (ii) sex ratio is not markedly affected across space and does not provide a reliable screening measure for detecting reproductive hazards ascribed to environmental factors.     

Efficient statistical mapping of avian count data

We develop a spatial modeling framework for count data that is efficient to implement in high-dimensional prediction problems. We consider spectral parameterizations for the spatially varying mean of a Poisson model. The spectral parameterization of the spatial process is very computationally efficient, enabling effective estimation and prediction in large problems using Markov chain Monte Carlo techniques. We apply this model to creating avian relative abundance maps from North American Breeding Bird Survey (BBS) data. Variation in the ability of observers to count birds is modeled as spatially independent noise, resulting in over-dispersion relative to the Poisson assumption. This approach represents an improvement over existing approaches used for spatial modeling of BBS data which are either inefficient for continental scale modeling and prediction or fail to accommodate important distributional features of count data thus leading to inaccurate accounting of prediction uncertainty.     

Modelling the distribution of plant species using the autologistic regression model

For modeling the distribution of plant species in terms of climate covariates, we consider an autologistic regression model for spatial binary data on a regularly spaced lattice. This model belongs to the class of autologistic models introduced by Besag (1974). Three estimation methods, the coding method, maximum pseudolikelihood method and Markov chain Monte Carlo method are studied and comparedvia simulation and real data examples. As examples, we use the proposed methodology to model the distributions of two plant species in the state of Florida.     

ANTIDEGRADATION WATER QUALITY CRITERIA FOR THE DELAWARE RIVER: A DISTRIBUTION-FREE STATISTICAL APPROACH1

ABSTRACT: Existing water quality for the Middle Delaware Scenic and Recreational River is significantly better than is required by current standards, leaving a potential for degradation. A method is presented for deriving candidate antidegradation water quality criteria for this segment of the Delaware River using statistical analysis of historic (ambient) water quality data. Data for 34 water quality parameters are first evaluated for data density, serial correlation, trend, seasonality, and other factors. These preliminary analyses are based on observation of data plots and application of distribution-free statistical techniques that are insensitive to outliers and are robust to relatively mild violations of basic assumptions. Data for 12 of the parameters have sufficient density for further analysis and can reasonably be modeled as independent and identically distributed over time (either seasonally or for the entire data sets). For these 12 parameters, distribution-free statistical methods are developed and used to derive intervals within which there is high confidence (usually greater than 95 percent) that the quantiles with potential use as anti-degradation criteria (the 0.85^th, 0.90^th, and 0.95^th quantiles in this study) for a particular parameter lie.     

REGIONALIZATION OF LOW-FLOW FREQUENCY ESTIMATES: AN ALABAMA CASE STUI)Y1

ABSTRACT: Low-flow estimates, as determined by probabilistic modeling of observed data sequences, are commonly used to describe certain streamflow characteristics. Unfortunately, however, reliable low-flow estimates can be difficult to come by, particularly for gaging sites with short record lengths. The shortness of records leads to uncertainties not only in the selection of a distribution for modeling purposes but also in the estimates of the parameters of a chosen model. In flood frequency analysis, the common approach to mitigation of some of these problems is through the regionalization of frequency behavior. The same general approach is applied here to the case of low-flow estimation, with the general intent of not only improving low-flow estimates but also illustrating the gains that might be attained in so doing. Data used for this study is that which has been systematically observed at 128 streamflow gaging sites across the State of Alabama. Our conclusions are that the log Pearson Type 3 distribution is a suitable candidate for modeling of Alabama low-flows, and that the shape parameter of that distribution can be estimated on a regional basis. Low-flow estimates based on the regional estimator are compared with estimates based on the use of only at-site estimation techniques.     

IMPROVED ESTIMATION OF ECOLOGICAL EFFECTS USING AN EMPIRICAL BAYES METHOD1

ABSTRACT: The US Environmental Protection Agency is currently developing guidance for assessing environmental impact using biocriteria within a regulatory framework. Of particular interest are statistical methods of design and analysis to test for impairment of biological assemblages in stream ecosystems associated with water pollution. Current recommendations emphasize frequentist statistical methods with the problem expressed as one of classical hypothesis testing. An empirical Bayes approach is proposed here as an alternative and applied for multi-site inference. The advantages of an empirical Bayes approach, in particular the substantive contribution of collateral information from nearby sites, are discussed in contrast to traditional methods that employ site-specific information only. The approach is illustrated in an application concerning trends in the Index of Biotic Integrity (IHI) for the Scioto River in Ohio.     

A WATERSHED-LEVEL ECOLOGICAL RISK ASSESSMENT METHODOLOGY1

ABSTRACT: We present an ecological risk assessment methodology at the watershed level for freshwater ecosystems. The major component is a pollutant transport and fate model (a modified EUTROMOD) with an integrated uncertainty analysis utilizing a two-phase Monte Carlo procedure. The uncertainty analysis methodology distinguishes between knowledge uncertainty and stochastic variability. The model assesses the ecological risk of lentic (lake) ecosystems in response to the stress of excess phosphorus resulting in eutrophication. The methodology and model were tested on the Wister Lake watershed in Oklahoma with the lake and its trophic state as the endpoint for ecological risk assessment. A geographic information system was used to store, manage, and manipulate spatially referenced data for model input.     

HYDROLOGIC UNCERTAINTY MEASURE AND NETWORK DESIGN1

ABSTRACT: This paper presents a simple methodology, using the entropy concept, to estimate regional hydro logic uncertainty and information at both gaged and ungaged grids in a basin. The methodology described in this paper is applicable for (a) the selection of the optimum station from a dense network, using maximization of information transmission criteria, and (b) expansion of a network using data from an existing sparse network by means of the information interpolation concept and identification of the zones from minimum hydrologic information. The computation of single and joint entropy terms used in the above two cases depends upon single and multivariable probability density functions. In this paper, these terms are derived for the gamma distribution. The derived formulation for optimum hydrologic network design was tested using the data from a network of 29 rain gages on Sleeper River Experimental Watershed. For the purpose of network reduction, the watershed was divided into three subregions, and the optimum stations and their locations in each subregion were identified. To apply the network expansion methodology, only the network consisting of 13 stations was used, and feasible triangular elements were formed by joining the stations. Hydrologic information was calculated at various points on the line segments, and critical information zones were identified by plotting information contours. The entropy concept used in this paper, although derived for single and bivaviate gamma distribution, is general in type and can easily be modified for other distributions by a simple variable transformation criterion.     

COMPARATIVE STUDY OF DROUGHT PREDICTION TECHNIQUES FOR RESERVOIR OPERATION1

ABSTRACT: Predicting the likelihood of a drought markedly enhances the efficiency of reservoir operations. This study applies the kriging method and time series analysis to predict inflows to Shihmen Reservoir in northern Taiwan. A subsequent reservoir operation simulation is employed to determine the drought lead time (DLT), the time before the onset of a drought. A more efficient reservoir operational strategy can be established with the aid of DLT and the probability of successful drought prediction (P s). Simulation results of reservoir operation over a period of three decades demonstrate that, at one month DLT, the kriging approach achieves 0.86 of P s for moderate droughts and 0.94 of P s for severe droughts. The kriging approach generally outperformed the time series approach in terms of DLT, P s of drought prediction, and the number of correctly predicted drought events.