Robust projection indices

Loosely speaking a robust projection index is one that prefers projections involving true clusters over projections consisting of a cluster and an outlier. We introduce a mathematical definition of one-dimensional index robustness and describe a numerical experiment to measure it. We design five new indices based on measuring divergence from Student's t -distribution which are intended to be especially robust: the experiment shows that they are more robust than several established indices. The experiment also reveals more generally that the robustness of moment indices depends on the number of approximation terms, providing additional practical guidance for existing projection pursuit implementations. We investigate the theoretical properties of one new Student t -index and Hall's index and show that the new index automatically adapts its robustness to the degree of outlier contamination. We conclude by outlining the possibilities for extending our experiments to both higher dimensions and other new indices.     

Total System Performance Assessment for Waste Disposal Using a Logic Tree Approach

The Electric Power Research Institute (EPRI) has sponsored the development of a model to assess the long-term, overall performance of the candidate spent fuel and high-level radioactive waste (HLW) disposal facility at Yucca Mountain, Nevada. The model simulates the processes that lead to HLW container corrosion, HLW mobilization from the spent fuel, and transport by groundwater, and contaminated groundwater usage by future hypothetical individuals leading to radiation doses to those individuals. The model must incorporate a multitude of complex, coupled processes across a variety of technical disciplines. Furthermore, because of the very long time frames involved in the modeling effort (10⁴ years), the relative lack of directly applicable data, and many uncertainties and variabilities in those data, a probabilistic approach to model development was necessary. The developers of the model chose a logic tree approach to represent uncertainties in both conceptual models and model parameter values. The developers felt the logic tree approach was the most appropriate. This paper discusses the value and use of logic trees applied to assessing the uncertainties in HLW disposal, the components of the model, and a few of the results of that model. The paper concludes with a comparison of logic trees and Monte Carlo approaches.     

Probabilistic Risk Analysis for a High-Level Radioactive Waste Repository

A probabilistic risk analysis (PRA) for a high-level radioactive waste repository is very important since it gives an estimate of its health impacts, allowing comparisons to be made with the health impacts of competing technologies. However, it is extremely difficult to develop a credible PRA for a specific repository site because of large uncertainties in future climate, hydrology, geological processes, etc. At best, such a PRA would not be understandable to the public. An alternative proposed here is to develop a PRA for an average U.S. site, taking all properties of the site to be the U.S. average. The results are equivalent to the average results for numerous randomly selected sites. Such a PRA is presented here; it is easy to understand, and it is not susceptible to substantial uncertainty. Applying the results to a specific repository site then requires only a simple, intuitively acceptable "leap of faith" in assuming that with large expenditures of effort and money, experts can select a site that would be at least as secure as a randomly selected site.     

A Mathematical Model for Pathogen Cross‐Contamination Dynamics during the Postharvest Processing of Leafy Greens

We developed a probabilistic mathematical model for the postharvest processing of leafy greens focusing on Escherichia coli O157:H7 contamination of fresh‐cut romaine lettuce as the case study. Our model can (i) support the investigation of cross‐contamination scenarios, and (ii) evaluate and compare different risk mitigation options. We used an agent‐based modeling framework to predict the pathogen prevalence and levels in bags of fresh‐cut lettuce and quantify spread of E. coli O157:H7 from contaminated lettuce to surface areas of processing equipment. Using an unbalanced factorial design, we were able to propagate combinations of random values assigned to model inputs through different processing steps and ranked statistically significant inputs with respect to their impacts on selected model outputs. Results indicated that whether contamination originated on incoming lettuce heads or on the surface areas of processing equipment, pathogen prevalence among bags of fresh‐cut lettuce and batches was most significantly impacted by the level of free chlorine in the flume tank and frequency of replacing the wash water inside the tank. Pathogen levels in bags of fresh‐cut lettuce were most significantly influenced by the initial levels of contamination on incoming lettuce heads or surface areas of processing equipment. The influence of surface contamination on pathogen prevalence or levels in fresh‐cut bags depended on the location of that surface relative to the flume tank. This study demonstrates that developing a flexible yet mathematically rigorous modeling tool, a “virtual laboratory,” can provide valuable insights into the effectiveness of individual and combined risk mitigation options.     

The cost of not knowing the radius

Robust Statistics considers the quality of statistical decisions in the presence of deviations from the ideal model, where deviations are modelled by neighborhoods of a certain size about the ideal model. We introduce a new concept of optimality (radius-minimaxity) if this size or radius is not precisely known: for this notion, we determine the increase of the maximum risk over the minimax risk in the case that the optimally robust estimator for the false neighborhood radius is used. The maximum increase of the relative risk is minimized in the case that the radius is known only to belong to some interval [r _l ,r _u ]. We pursue this minmax approach for a number of ideal models and a variety of neighborhoods. Also, the effect of increasing parameter dimension is studied for these models. The minimax increase of relative risk in case the radius is completely unknown, compared with that of the most robust procedure, is 18.1% versus 57.1% and 50.5% versus 172.1% for one-dimensional location and scale, respectively, and less than 1/3 in other typical contamination models. In most models considered so far, the radius needs to be specified only up to a factor , in order to keep the increase of relative risk below 12.5%, provided that the radius–minimax robust estimator is employed. The least favorable radii leading to the radius–minimax estimators turn out small: 5–6% contamination, at sample size 100.      

构建中国的排污权交易制度

由于中国现阶段法制不健全、信用机制和市场机制不完善,政府按照行政区划对污染物进行管理和控制,排污权交易制度到目前为止没有在中国形成一项正式的法律制度或政策。因此,在学习国外先进经验的基础上探讨排污权交易的原则、主体、对象、方式、监督和法律责任,对建立中国的排污权交易制度具有重要的理论意义和现实意义。     

Interpretation of Monte Carlo Simulations Using Parameter Space Plots

Multimodal distribution functions that result from Monte Carlo simulations can be interpreted by superimposing joint probability density functions onto the contour space of the simulated calculations. The method is demonstrated by analysis of the pathway of a radioactive groundwater contaminant using an analytical solution to the transport equation. Simulated concentrations at a fixed time and distance produce multimodal histograms, which are understood with reference to the parameter space for the two random variables-velocity and dispersivity. Numerical integration under the joint density function up to the contour of the analytical solution gives the probability of contaminant exceeding a target concentration. This technique is potentially more efficient than Monte Carlo simulation for low probability events. Visualization of parameter space is restricted to two random variables. Nevertheless, analyzing the two most pertinent random variables in a simulation might still offer insights into the multimodal nature of output histograms.     

A FULLY NONPARAMETRIC TEST FOR ONE-WAY LAYOUTS

The use of a vector of sign statistics as the basis of a nonparametric test for equality of distributions in one‐way layouts is considered. An important feature of this test is its ability to detect a broad range of alternatives, including scale and shape differences. In this scenario, the data consist of several independent measurements on each treatment or subject. Presented here are a finite sample and asymptotic distribution theory for the test statistics and a discussion of a follow‐up clustering procedure based on a mixture model approximation. Finally, the methods are illustrated using two examples from the literature.     

Methodology for setting risk-based concentrations of contaminants in soil and groundwater and application to a model contaminated site

In Japan, environmental standards for contaminants in groundwater and in leachate from soil are set with the assumption that they are used for drinking water over a human lifetime. Where there is neither a well nor groundwater used for drinking, the standard is thus too severe. Therefore, remediation based on these standards incurs excessive effort and cost. In contrast, the environmental-assessment procedure used in the United States and the Netherlands considers the site conditions (land use, existing wells, etc.); however, a risk assessment is required for each site. Therefore, this study proposes a new framework for judging contamination in Japan by considering the merits of the environmental standards used and a method for risk assessment. The framework involves setting risk-based concentrations that are attainable remediation goals for contaminants in soil and groundwater. The framework was then applied to a model contaminated site for risk management, and the results are discussed regarding the effectiveness and applicability of the new methodology.     

Hierarchical Bayesian models to assess between- and within-batch variability of pathogen contamination in food

Assessing within-batch and between-batch variability is of major interest for risk assessors and risk managers in the context of microbiological contamination of food. For example, the ratio between the within-batch variability and the between-batch variability has a large impact on the results of a sampling plan. Here, we designed hierarchical Bayesian models to represent such variability. Compatible priors were built mathematically to obtain sound model comparisons. A numeric criterion is proposed to assess the contamination structure comparing the ability of the models to replicate grouped data at the batch level using a posterior predictive loss approach. Models were applied to two case studies: contamination by Listeria monocytogenes of pork breast used to produce diced bacon and contamination by the same microorganism on cold smoked salmon at the end of the process. In the first case study, a contamination structure clearly exists and is located at the batch level, that is, between batches variability is relatively strong, whereas in the second a structure also exists but is less marked.