Nonparametric mean estimation using partially ordered sets

In ranked-set sampling (RSS), the ranker must give a complete ranking of the units in each set. In this paper, we consider a modification of RSS that allows the ranker to declare ties. Our sampling method is simply to break the ties at random so that we obtain a standard ranked-set sample, but also to record the tie structure for use in estimation. We propose several different nonparametric mean estimators that incorporate the tie information, and we show that the best of these estimators is substantially more efficient than estimators that ignore the ties. As part of our comparison of estimators, we develop new results about models for ties in rankings. We also show that there are settings where, to achieve more efficient estimation, ties should be declared not just when the ranker is actually unsure about how units rank, but also when the ranker is sure about the ranking, but believes that the units are close.     

Multiple indicators, partially ordered sets, and linear extensions: Multi-criterion ranking and prioritization

This paper is concerned with the question of ranking a finite collection of objects when a suite of indicator values is available for each member of the collection. The objects can be represented as a cloud of points in indicator space, but the different indicators (coordinate axes) typically convey different comparative messages and there is no unique way to rank the objects while taking all indicators into account. A conventional solution is to assign a composite numerical score to each object by combining the indicator information in some fashion. Consciously or otherwise, every such composite involves judgments (often arbitrary or controversial) about tradeoffs or substitutability among indicators. Rather than trying to combine indicators, we take the view that the relative positions in indicator space determine only a partial ordering and that a given pair of objects may not be inherently comparable. Working with Hasse diagrams of the partial order, we study the collection of all rankings that are compatible with the partial order (linear extensions). In this way, an interval of possible ranks is assigned to each object. The intervals can be very wide, however. Noting that ranks near the ends of each interval are usually infrequent under linear extensions, a probability distribution is obtained over the interval of possible ranks. This distribution, called the rank-frequency distribution, turns out to be unimodal (in fact, log-concave) and represents the degree of ambiguity involved in attempting to assign a rank to the corresponding object. Stochastic ordering of probability distributions imposes a partial order on the collection of rank-frequency distributions. This collection of distributions is in one-to-one correspondence with the original collection of objects and the induced ordering on these objects is called the cumulative rank-frequency (CRF) ordering; it extends the original partial order. Although the CRF ordering need not be linear, it can be iterated to yield a fixed point of the CRF operator. We hypothesize that the fixed points of the CRF operator are exactly the linear orderings. The CRF operator treats each linear extension as an equal voter in determining the CRF ranking. It is possible to generalize to a weighted CRF operator by giving linear extensions differential weights either on mathematical grounds (e.g., number of jumps) or empirical grounds (e.g., indicator concordance). Explicit enumeration of all possible linear extensions is computationally impractical unless the number of objects is quite small. In such cases, the rank-frequencies can be estimated using discrete Markov chain Monte Carlo (MCMC) methods.     

A method to reconstruct anguilliform fishes from partially digested items

Estimating the amounts of resources consumed by individuals is important in many studies. For predators, allometric relationships can be used to extrapolate the size of preys from undigested remains found in the stomach and in the faeces. However, such equations are available for a limited number of species. Based on a large sample size gathered in New Caledonia on both predators (sea kraits) and their preys (anguilliform fishes), we provide the first allometric relationships that allow estimating accurately the mass and the size of various anguilliform fish species.     

Estimating historic movement of a climatological variable from a pair of misaligned functional data sets

Environmental and Ecological Statistics - We consider the problem of estimating the mean function from a pair of paleoclimatic functional data sets after one of them has been registered with the...     

Radial basis function networks with partially classified data

The problem of estimating a classification rule with partially classified observations, which often occurs in biological and ecological modelling, and which is of major interest in pattern recognition, is discussed. Radial basis function networks for classification problems are presented and compared with the discriminant analysis with partially classified data, in situations where some observations in the training set are unclassified. An application on a set of morphometric data obtained from the skulls of 288 specimens of Microtus subterraneus and Microtus multiplex is performed. This example illustrates how the use of both classified and unclassified observations in the estimate of the hidden layer parameters has the potential to greatly improve the network performances.     

Conjugate depths in partially filled sewers and pipes

Environmental Fluid Mechanics - Partially filled pipes have many applications in hydraulic and environmental engineering; such as sewer and storm water collection pipes and circular culverts....     

Optimizing model for land use/land cover retrieval from remote sensing imagery based on variable precision rough sets

The suitable spectral mode in remote sensing is often desirable to facilitate the inversion of ecological environment and landscape. This paper put forward an optimizing model based on variable precision rough sets (VPRS) for the land cover discrimination in wetland inventory. In the case study of Lake Baiyangdian which has important ecological functions to the northern China, this model is established successfully according to the domain-experts knowledge. The procedure is as follows. First step is data collection, including remote-sensing data (e.g., Landsat-5 TM bands), the digitized relief maps, and statistical yearbooks. Second, the remote sensing imagery (RSI) and relief maps are co-registered into the same resolution. Third, a condition set, including various attributes is derived from spectral bands, band math or ratio indices based on previous studies, at the same time, the decision set is derived from true land types after investigation and validation. Then, the remote sensing decision table (RSDT) is constructed by linking condition set with decision set according to the sequential pixels in RSI. Fourth, we create one forward greedy searching algorithm based on VPRS to handle this RSDT. After adjusting parameters such as β and knowledge granularity diameter (KGD), we obtain the stable optimized results. Comparative experiments and evaluation show that the discrimination or retrieval accuracy of VPRS model is satisfying (overall accuracy: 87.32% and KHAT: 0.84) and better than original data. Moreover, data dimension has been decreased dramatically (from 12 to 3) and key attributes found by the model may be useful for specific retrieval in wetland inventories.     

Sampling designs on stream networks using the pseudo-Bayesian approach

Monitoring stream networks through time provides important ecological information. The sampling design problem is to choose locations where measurements are taken so as to maximise information gathered about physicochemical and biological variables on the stream network. This paper uses a pseudo-Bayesian approach, averaging a utility function over a prior distribution, in finding a design which maximizes the average utility. We use models for correlations of observations on the stream network that are based on stream network distances and described by moving average error models. Utility functions used reflect the needs of the experimenter, such as prediction of location values or estimation of parameters. We propose an algorithmic approach to design with the mean utility of a design estimated using Monte Carlo techniques and an exchange algorithm to search for optimal sampling designs. In particular we focus on the problem of finding an optimal design from a set of fixed designs and finding an optimal subset of a given set of sampling locations. As there are many different variables to measure, such as chemical, physical and biological measurements at each location, designs are derived from models based on different types of response variables: continuous, counts and proportions. We apply the methodology to a synthetic example and the Lake Eacham stream network on the Atherton Tablelands in Queensland, Australia. We show that the optimal designs depend very much on the choice of utility function, varying from space filling to clustered designs and mixtures of these, but given the utility function, designs are relatively robust to the type of response variable.     

Sampling behavior of starlings foraging in simple patchy environments

Summary Starlings were allowed to forage in patchy laboratory environments where patches contained either zero or a fixed number of prey. The condition of a given patch (prey or no prey) could only be determined from information gained while exploiting the patch. A starling's task was to determine to what extent to sample an apparently prey-less patch before giving it up as such, in a way which maximizes long-term energy intake rate. The simple model presented to predict the optimal sampling solutions was qualitatively but not quantitatively supported by the data. The main discrepancy was in the fact that an apparently prey-less patch should have been sampled to a fixed extent before leaving, whereas a distribution of sampling behavior was actually observed. The qualitative agreement was very good, however, as the modes of the observed sampling distributions often corresponded to the predicted optimal sampling solutions. Starlings seem to possess a patch-sampling ability which, at least for those simple situations analyzed, can lead to an efficient foraging strategy.     

大气污染源监测采样技术

依据气态污染源共同的排放特性及平均排放浓度，排放速率的概念，导出气态污染源监测中常用的三种采样方法：积分法、分部积分法、有限加合近似法。根据分析化学的要求，提出样品采集时间的设计方法。由此得出不同类型排放源的监测时间和采样频率确定方法。     

Sampling of airborne polycyclic aromatic hydrocarbons with semipermeable membrane devices

Semipermeable membrane devices (SPMDs) are nowadays used as passive samplers of organic pollutants. The knowledge of the sampling rate values (R_S) of each substance trapped on membranes is necessary to calculate their average concentration. Here we calculate R_S values for 16 polycyclic aromatic hydrocarbons using the comparison of active sampling method results and the amounts sequestered by SPMDs at varying exposure times.Selected article from the Regional Symposium on Chemistry and Environment, Krusevac, Serbia, June 2003, organized by Dr. Branimir Jovancicevic.     

Using Niche-Based Models to Improve the Sampling of Rare Species

Abstract:  Because data on rare species usually are sparse, it is important to have efficient ways to sample additional data. Traditional sampling approaches are of limited value for rare species because a very large proportion of randomly chosen sampling sites are unlikely to shelter the species. For these species, spatial predictions from niche-based distribution models can be used to stratify the sampling and increase sampling efficiency. New data sampled are then used to improve the initial model. Applying this approach repeatedly is an adaptive process that may allow increasing the number of new occurrences found. We illustrate the approach with a case study of a rare and endangered plant species in Switzerland and a simulation experiment. Our field survey confirmed that the method helps in the discovery of new populations of the target species in remote areas where the predicted habitat suitability is high. In our simulations the model-based approach provided a significant improvement (by a factor of 1.8 to 4 times, depending on the measure) over simple random sampling. In terms of cost this approach may save up to 70% of the time spent in the field.     

Sampling for weed spatial distribution mapping need not be adaptive

Weeds are species of interest for ecologists because they are competitors of the crop for resources but they also play an important role in maintaining biodiversity in agroecosystems. To study their spatial distribution at the field scale, only sampled observations are available due to the cost of sampling. Weeds sampling strategies are static. However, in the domain of spatial sampling, adaptive strategies have also been developed with, for some of them, an important on-line or off-line computational cost. In this article we provide answers to the following question: Are the current adaptive sampling methods efficient enough to motivate a wider use in practice when sampling a weed species at a field scale? We provide a comparison of the behaviour of 8 static strategies and 3 adaptive ones on four criteria: density class estimation, map restoration, spatial aggregation estimation, and sampling duration. From two weeds data sets, we estimated six contrasted Markov Random Field (MRF) models of weed density class spatial distribution and a model for sampling duration. The MRF models were then used to compare the strategies on a large set of simulated maps. Our main finding was that there is no clear gain in using adaptive sampling strategies rather than static ones for the three first criteria, and adaptive strategies were associated to longer sampling duration. This conclusion points out that for weed mapping, it is more important to build a good model of spatial distribution, than to propose complex adaptive sampling strategies.     

Science or Slaughter: Need for Lethal Sampling of Sharks

Abstract: General consensus among scientists, commercial interests, and the public regarding the status of shark populations is leading to an increasing need for the scientific community to provide information to help guide effective management and conservation actions. Experience from other marine vertebrate taxa suggests that public, political, and media pressures will play an increasingly important part in setting research, management, and conservation priorities. We examined the potential implications of nonscientific influences on shark research. In particular, we considered whether lethal research sampling of sharks is justified. Although lethal sampling comes at a cost to a population, especially for threatened species, the conservation benefits from well‐designed studies provide essential data that cannot be collected currently in any other way. Methods that enable nonlethal collection of life‐history data on sharks are being developed (e.g., use of blood samples to detect maturity), but in the near future they will not provide widespread or significant benefits. Development of these techniques needs to continue, as does the way in which scientists coordinate their use of material collected during lethal sampling. For almost half of the known shark species there are insufficient data to determine their population status; thus, there is an ongoing need for further collection of scientific data to ensure all shark populations have a future. Shark populations will benefit most when decisions about the use of lethal sampling are made on the basis of scientific evidence that is free from individual, political, public, and media pressures.     

Sampling animal association networks with the gambit of the group

Ecologists increasingly use network theory to examine animal association patterns. The gambit of the group (GoG) is a simple and useful assumption for accumulating the data necessary for a network analysis. The gambit of the group implies that each animal in a group is associating with every other individual in that group. Sampling is an important issue for networks in wild populations collected assuming GoG. Due to time, effort, and resource constraints and the difficulty of tracking animals, sampled data are usually a subset of the actual network. Ecologists often use association indexes to calculate the frequency of associations between individuals. These indexes are often transformed by applying a filter to produce a binary network. We explore GoG sampling using model networks. We examine assortment at the level of the group by a single dichotomous trait, along with many other network measures, to examine the effect of different sampling regimes, and choice of filter on the accuracy and precision with which measures are estimated. We find strong support for the use of weighted, rather than filtered, network measures and show that different filters have different effects depending on the nature of the sampling. We make several practical recommendations for ecologists planning GoG sampling.     

Lateral velocity distribution in open channels with partially flexible submerged vegetation

Environmental Fluid Mechanics - This study implemented three analytical models to investigate the lateral distribution of depth-averaged streamwise velocity in a rectangular channel with lateral,...