Statistics and uncertainty

Quantitative Microbial Risk Assessment Institute HandbookThis chapter provides a review of concepts from probability and statistics that are useful for risk assessment. It begins with a review of probability density distribution functions, then covers how these functions are used as models for variability and uncertainty in risk assessment, describes how these functions are fit to it particular cases by estimating parameters, and describes one method, bootstrapping, for quantifying uncertainty in these parameter estimates

Making sense of the benefit-cost provisions of the Safe Drinking Water Act

Paper presented at the AWWA Annual Conference and Exposition, Orlando, FL .Prior to 1996, drinking water standards were required to be as close to absolutely protective of human health as technically and economically feasible. The 1996 Amendments to the Safe Drinking Water Act gave EPA the option to set standards that are less protective than feasible, based on benefit-cost criteria. However, the 1996 Amendments do not simply instruct EPA to maximize net benefits, as is typical in an economic benefit-cost assessment. Instead EPA is instructed to "maximize health risk reduction benefits at a cost that is justified by the benefits". Exactly what this means is unclear. Many commentators on EPA rules base their evaluations on maximizing net benefits. In contrast, EPA has explicitly rejected simple maximization of net benefits by citing the priority given to health risk reduction in its legislative mandate. This study considers the impacts of different interpretations of the benefit-cost provisions of the 1996 Amendments. It concludes that the use of a higher monetary value for risk reduction than that currently used by EPA would more closely reflect the statutory preference for health benefits. However, the author does not advocate this as the preferred decision-making criterion. Instead an alternative procedure is described in which preference is given for outcomes likely to have positive net benefits over outcomes for which there is substantial uncertainty as to whether the net benefits will be positive. This approach will favor less dramatic regulatory actions in the short term, while allowing for more stringent regulations as uncertainties are reduced over time

Microfiltration Cost Benchmarking for Large Facilities

A number of models of the cost of microfiltration treatment exist, but these models generally do not address, or are not validated for, larger facilities (facilities with design flow of 5 mgd or greater). In the past, microfiltration was not cost-competitive for larger facilities, but it is now being adopted at plants with design flows as large as 20 mgd. Accordingly, there is a need to extend these cost models to include larger facilities. Data for the larger facilities is still somewhat sparse, as only a few have yet been constructed. Nevertheless, the information that is available on these facilities can provide a valuable guide as to the economies of scale that may be available to larger treatment plants. In this study a survey of costs at large microfiltration plants was conducted. Data was obtained for 10 facilities, including 3 facilities with design flows greater than 9 mgd. The results indicate that large systems can achieve economies of scale, despite the modular nature of most microfiltration units. The three largest facilities (design flows of 9 to 20 mgd) have costs of less than 50 cents/thousand gallons. The cost estimates for facilities with flows of less than 5 mgd closely match a previous survey of small microfiltration plants. In addition, this study provides a basis for extending the predictions of existing cost models up to design flows of 20 mgd. Results indicate that costs vary among systems of the same capacity with 95% of all systems being within roughly a factor of two of the mean cost

Economic analysis of decentralized options for providing water service to low-income settlements

The U.S.-Mexico border region has large numbers of unincorporated settlements lacking basic services, which are known as colonias. Sanitation and health conditions in colonias can be compared to those in third world countries. El Paso County has approximately 200 known colonias. Despite large-scale investments to extend water supply to the colonias, approximately 3500 colonia residents still lack piped water service. Extending service to these remaining residents would be prohibitively expensive. A previous study estimated that providing piped water supply would cost an average of $119,000 per lot. In this study, a representative colonia with an estimated population of 558 residents is evaluated to determine the costs of de-centralized approaches to water supply. A survey was administered to document the costs the residents currently pay for delivery by truck. Household water bills were found to average$808 annually, confirming that the predominantly low-income colonia residents pay more for water than do households served by piped water supplies. A cost comparison of the current water supply delivery cost vs. the proposed cost of well drilling was performed to determine if it is economically feasible to construct wells. The well construction option is estimated to have an initial investment of $13,980 and a capital recovery period of 6 years. Therefore, the construction of wells appears to be an appropriate option for colonia residents

Spatial Trends in Groundwater Arsenic Concentrations

Arsenic presents complex spatial occurrence trends that can be difficult to identify and understand. This project sought to understand geographic trends in arsenic occurrence using a visualization technique. The approach taken was to link geospatially referenced arsenic concentration information from a water quality database with elevation data contained in Digital Terrain Elevation Data (DTED) files. DTED files are available for all land masses across the world for public download. This allows for the development of three-dimensional plots of arsenic concentration and topography. The plots developed in this manner show that high arsenic is associated with the transition from plains to piedmont on the western side of the Delaware River Valley in New Jersey. In Oklahoma high arsenic is found along the North Canadian River Valley. In New Mexico high concentrations are generally high in the Rio Grande Valley but with an area of low concentration in the southern portion of this valley. In California, arsenic concentrations are high in the middle of the Central Valley but moderate somewhat toward the edges. These results are consistent with mobilization of arsenic by reductive processes in the organic-rich sediments of river valleys, but further statistical analysis is required to confirm the significance of this association. The visualization software used here is broadly applicable and a user guide for this software is available on request