Balch M.S.,Applied Biomathematics, Inc.
International Journal of Approximate Reasoning | Year: 2012
This paper introduces a new mathematical object: the confidence structure. A confidence structure represents inferential uncertainty in an unknown parameter by defining a belief function whose output is commensurate with Neyman-Pearson confidence. Confidence structures on a group of input variables can be propagated through a function to obtain a valid confidence structure on the output of that function. The theory of confidence structures is created by enhancing the extant theory of confidence distributions with the mathematical generality of Dempster-Shafer evidence theory. Mathematical proofs grounded in random set theory demonstrate the operative properties of confidence structures. The result is a new theory which achieves the holistic goals of Bayesian inference while maintaining the empirical rigor of frequentist inference. © 2012 Elsevier Inc. All rights reserved.
Beer M.,University of Liverpool |
Ferson S.,Applied Biomathematics, Inc. |
Kreinovich V.,University of Texas at El Paso
Mechanical Systems and Signal Processing | Year: 2013
Probabilistic uncertainty and imprecision in structural parameters and in environmental conditions and loads are challenging phenomena in engineering analyses. They require appropriate mathematical modeling and quantification to obtain realistic results when predicting the behavior and reliability of engineering structures and systems. But the modeling and quantification is complicated by the characteristics of the available information, which involves, for example, sparse data, poor measurements and subjective information. This raises the question whether the available information is sufficient for probabilistic modeling or rather suggests a set-theoretical approach. The framework of imprecise probabilities provides a mathematical basis to deal with these problems which involve both probabilistic and non-probabilistic information. A common feature of the various concepts of imprecise probabilities is the consideration of an entire set of probabilistic models in one analysis. The theoretical differences between the concepts mainly concern the mathematical description of the set of probabilistic models and the connection to the probabilistic models involved. This paper provides an overview on developments which involve imprecise probabilities for the solution of engineering problems. Evidence theory, probability bounds analysis with p-boxes, and fuzzy probabilities are discussed with emphasis on their key features and on their relationships to one another. This paper was especially prepared for this special issue and reflects, in various ways, the thinking and presentation preferences of the authors, who are also the guest editors for this special issue. © 2013 Elsevier Ltd.
Sentz K.,Los Alamos National Laboratory |
Ferson S.,Applied Biomathematics, Inc.
Reliability Engineering and System Safety | Year: 2011
The current challenge of nuclear weapon stockpile certification is to assess the reliability of complex, high-consequent, and aging systems without the benefit of full-system test data. In the absence of full-system testing, disparate kinds of information are used to inform certification assessments such as archival data, experimental data on partial systems, data on related or similar systems, computer models and simulations, and expert knowledge. In some instances, data can be scarce and information incomplete. The challenge of Quantification of Margins and Uncertainties (QMU) is to develop a methodology to support decision-making in this informational context. Given the difficulty presented by mixed and incomplete information, we contend that the uncertainty representation for the QMU methodology should be expanded to include more general characterizations that reflect imperfect information. One type of generalized uncertainty representation, known as probability bounds analysis, constitutes the union of probability theory and interval analysis where a class of distributions is defined by two bounding distributions. This has the advantage of rigorously bounding the uncertainty when inputs are imperfectly known. We argue for the inclusion of probability bounds analysis as one of many tools that are relevant for QMU and demonstrate its usefulness as compared to other methods in a reliability example with imperfect input information. © 2011 Elsevier Ltd. All rights reserved.
Agency: Department of Defense | Branch: Missile Defense Agency | Program: STTR | Phase: Phase I | Award Amount: 99.27K | Year: 2013
An emerging consensus in engineering holds that aleatory uncertainty should be propagated by traditional methods of probability theory but that epistemic uncertainty may require methods that do not confuse incertitude with variability by requiring every possibility be associated with a probability that it occurs. Therefore, although Monte Carlo shells that re-run calculations many times while varying input values according to specified distributions are useful, they are insufficient to properly account for epistemic and aleatory uncertainty. Three things are needed to build on the new consensus. The first is a clear and comprehensive roadmap for how various important problems (e.g., arithmetic and logical evaluations, backcalculations, sensitivity analyses, etc.) can be solved under this view. The second is software that enables analysts to automatically propagate through simulations the uncertainty implied by the significant digits of the numbers specifying a model. Such software would require very little training in uncertainty analysis to be useful to analysts. The third need is a software library of recommended methods for common calculations that is usable by modelers and analysts who may not themselves be experts in uncertainty quantification but who recognize the need for and benefits from it.
Agency: Department of Health and Human Services | Branch: | Program: SBIR | Phase: Phase I | Award Amount: 480.87K | Year: 2012
DESCRIPTION (provided by applicant): Patient data collected during health care delivery and public health surveys possess a great deal of information that could be used in biomedical and epidemiological research. Access to these data, however, is usually limited because of the private nature of most personal health records. Methods of balancing the informativeness of data for research with the information loss required to minimize disclosure risk are needed before these data can be used to improve public health. Current methods are primarily focused on protecting privacy, but focusing on protecting privacy alone is inadequate. In statistical disclosure control techniques, information truthfulness is not well preserved so that unreliable results may be released. In generalization-based anonymization approaches, there is information loss due to attribute generalization and existing techniques do not provide sufficient control for maintaining data utility. What are currently needed are methods that protect boththe privacy of individuals represented in the data as well as the integrity of relationships studied by researchers. The problem is that there is an inherent tradeoff between protecting the privacy of individuals and protecting the informativeness of the data set. Protecting the privacy of individuals always results in a loss of information and it is the information contained by the data set that affects the power of a statistical test. For a given anonymization strategy, however, there are often multiple ways of masking the data that meet the disclosure risk criteria provided. This can be taken advantage of to choose the solution that best preserves statistical information while meeting the disclosure risk criteria provided. This project will develop the first integrated software system that provides solutions for problems faced in all three stages in the release of sensitive health care data: 1. anonymize a data set by intervalizing/generalizing data to satisfy currently available anonymization strategies,2. provide sufficient controls within anonymization procedures to satisfy constraints on statistical usefulness of the data, and 3. compute statistical tests for the anonymized data intervals. There are two main challenges facing this effort. The first isthat, based on existing research results, integrating our proposed new control processes into anonymization procedures is expected to be computationally difficult. We will overcome this challenge by developing efficient and practically useful greedy algorithms, approximation algorithms, or algorithms working for realistic situations (if not for general cases). The other primary challenge facing this effort is the fact that statistical calculations with interval data sets are known to be computationally difficult, and these calculations are necessary both for control processes within anonymization procedures and for subsequent statistical computation and tests. We will overcome this challenge with efficient algorithms that exploit the structure present in data sets intervalized for privacy. The software will be tested on medical data sets of various sizes and structures to demonstrate the feasibility of the approach and to characterize the scalability of the algorithms with data set size. PUBLIC HEALTHRELEVANCE: Patient health records possess a great deal of information that is useful in medical research, but access to these data is usually limited because of the private nature of most personal health records. Methods of balancing the informativeness ofdata for research with the information loss required to minimize disclosure risk are needed before these data can be used to improve public health. This project will develop the first integrated software system that provides solutions for intervalizing/generalizing data, controlling data utility, and performing analyses using interval statistics.
Agency: Department of Agriculture | Branch: | Program: SBIR | Phase: Phase II | Award Amount: 600.00K | Year: 2016
1. Crops that have been genetically modified to protect against insect pests, such as those expressing Bt toxins, have gained tremendous economic and societal importance. These biotechnology products improve the stability of agricultural production through highly effective crop protection while reducing the use of traditional pesticides, fuel, and water by farmers in the US and internationally. Significantly, Bt technology has improved economic outcomes for growers. However, the durability of any given Bt toxin as a protective agent is shortened by the evolution of resistance in the target pest population. Strategies for delaying the evolution of resistance, called insect resistance mangement (IRM), need to be paired intelligently with the crop type, the climate, the target pest, and local agricultural practices. Research into IRM increasingly relies on sophisticated mathematical models that allow many numerical experiments to be done in a short amount of time. The complexity of these models has brought about a number of drawbacks, including 1) inconsistent assumptions that make model comparison difficult, 2) a lack of transparency due to the sheer difficulty of reproducing these models, and 3) the limitation of IRM modeling to a relatively small number of highly skilled researchers.With this USDA-NIFA SBIR Phase II award, Applied Biomathematics intends to research and develop the computational algorithms necessary to support a program that allows users to model the evolution of resistance to Bt or similar transgenic technologies in complex, multi-crop landscapes for a wide variety of target pests. The main goal of the project is to build a simulation engine capable of tracking responses to selection for resistance at up to 12 different genes, each of which may be associated with resistance to one or more Bt toxins. This task is difficult because such genetic complexity can consume a large amount of computing power and memory. Making the performance of the program good enough to use on typical computing platforms requires careful and creative optimization. Our approach will mix algorithms that simulate individual pests in great detail when necessary with faster approaches that lump individuals into populations with similar characteristics. This approach will be faster than models that are purely individual based but should preserve biological detail better than population-level approximations typically used in models with more than one gene. As part of a program that allows users to build IRM models without special training in mathematics, population genetics, or programming and that defines IRM models through a standard set of user inputs, the improved genetics algorithm will lead to a simulation tool that is powerful, transparent, and widely accessible.
Agency: Department of Agriculture | Branch: | Program: SBIR | Phase: Phase I | Award Amount: 100.00K | Year: 2015
There is a growing body of evidence that neonicotinoid based insecticides are partly responsible for the so-called bee colony collapse disorder in which entire colonies of Western honey bees die off. However, many experts believe that more scientific research is needed before supporting a ban of these pesticides to take them off the market. Seacoast is developing an innovative analytical device to allow more frequent field measurements and reduce costs associated with pesticide monitoring. This portable detection device targets the detection of neonicotinoids on crops and soil and can be expanded to analyze a wide range of other pesticides. The analytical instrument is compact for field applications, low-cost, and easy-to-use to permit wide-range measurement of the insecticide's presence. Most importantly, the system design is based on well established chromatography principles with a highly sensitive detector module. This proposal presents both novel instrument design and materials engineering approaches to conceive a field useable neonicotinoid analyzer with sufficient analytical power but ease-of-use for broad applicability. To accomplish the proposed objectives, Seacoast Science, Inc. is partnering with Colnatec, LLC, two small sized technology companies, to combine their expertise in instrument design and high sensitivity sensor systems. The innovative analyzer is composed of Seacoast's next generation miniature gas chromatograph with Colnatec's advanced, high-resolution quartz crystal microbalance sensor. The system is designed to operate predominately with ambient air as the carrier gas with single parts-per-billion sensitivities.The economic impact of the decline of honeybee colonies ranges in the billions of dollars due to the reduction of effectively pollinated crops. Researchers approximate that nearly one-third of all honey bee colonies in the US have vanished. To protect its bees, Europe banned the use of neonicotinoid pesticides last year, while U.S. authorities have so far taken a more cautious approach in gaining more scientific data on the presence of these insecticides throughout the agricultural landscape. The early adopters of Seacoast's proposed neonicotinoid detection system include large industrial farms and nurseries, beekeepers and academic and federal research groups; a $12M market, but with the expansion of the analyzer into the broader pesticide detection market, the market size grows to >$18M accordingly.
Agency: Department of Agriculture | Branch: | Program: SBIR | Phase: Phase I | Award Amount: 100.00K | Year: 2015
Bt crops offer tremendous potential benefits to growers, the environment, seed companies, and society. The risk of pest resistance threatens to reduce the benefits of Bt technology, including its profitability. Mathematical models of evolution provide the main tool guiding insect resistance management (IRM). IRM models are used to quantify and communicate the benefits of stewardship practices. The EPA requires registrants of new Bt crops in the United States to support IRM plans with models that can forestall the evolution of resistance. Models are also increasingly used internally in industry to inform product design and strategy. Currently, a patchwork of in-house, outsourced, and published models are used to assess the risk of resistance evolution on a case-by-case basis. A common modeling platform would increase the efficiency of research and regulation and the advisory role USDA plays to growers and EPA while promoting transparency and uniform scientific standards. Focused development of a common modeling platform is also an opportunity to surpass the capabilities of existing models with features that address current and near-future needs, such as increased genetic complexity.The proposed research will determine the feasibility of producing an IRM modeling platform that matches or exceeds the capabilities of existing models in use by industry, academic, and government scientists while being flexible enough for diverse applications. Feasibility will be tested using a prototype software framework to reproduce 3 published IRM models addressing different biological questions. Close review of a larger set of 10 studies will also serve to identify and prioritize additional software features for development in Phase II. Development of a second prototype aimed at greater genetic complexity will investigate the feasibility of obtaining uniform results from multiple modeling frameworks.The initial target users of the proposed software platform are modelers in industry, academics and government. We expect to also quickly enter the market for graduate-level research and education. Future development of derivative products will target users in introductory and advanced undergraduate education. In our company's experience, accessible modeling tools not only achieve their intended direct benefits but also lead to job creation through greater investment in modeling and a better-educated work force.
Agency: Department of Agriculture | Branch: | Program: SBIR | Phase: Phase II | Award Amount: 450.00K | Year: 2014
Human land-use decisions can adversely affect the vitality and diversity of natural communities. However, well-designed regional development plans can mitigate or even reverse biodiversity losses. This project aims to develop methods and software for evaluating the effects of human landusedecisions on biodiversity.The proposed work will enable rapid assessment of the biodiversity consequences of alternative development and conservation strategies, extending Applied Biomathematics & #39; internationally recognized technologies for modeling the viability of spatiallystructured wildlife populations. The software will generate a temporal progression of habitat qualitymaps with which the viability of a suite of selected species is assessed. The habitat dynamicsmodule integrates land-use and conservation decision rules with other habitat change processes,harnessing existing data and models on human demography, wildlife habitat, and climate change.Major advances of the proposed software include the ability to specify interactions among thenatural and anthropogenic drivers of landscape change, and the ability to assess conservation tradeoffsin a multi-species framework. Users will be able to employ this framework to make informeddecisions regarding regional development, management, restoration and wildlife protection.The proposed software will be marketed to federal, state, and local planning and regulatoryagencies, international agencies, universities, non-profit organizations, and environmentalconsultants. We believe the product will contribute substantially to the protection and enhancementof the nation & #39;s natural heritage by providing an objective, interactive, and transparent framework forassessing the biodiversity consequences of alternative land-use strategies.
Agency: Department of Agriculture | Branch: | Program: SBIR | Phase: Phase II | Award Amount: 349.98K | Year: 2009
Forest insect pests cause significant economic and ecological damage every year. Dramatically increased pest activity in recent years suggests that changing climate conditions will inflate the uncertainty associated with pest risk assessments. Advances in forest pest risk analysis methodology are needed to allow managers to better explore the consequences and value of alternative management scenarios and to facilitate improvements in the prioritization of threats to natural resources. Although tools are currently available for mapping the risk of pest activity according to landscape features, host distributions, and climate, most equate habitat suitability with risk. A necessary but underdeveloped way to improve risk assessments would incorporate information about population dynamics. We propose to develop the first software tool that will accept a wide range of GIS-based factors, including habitat suitability maps, and predict risk based on spatially explicit simulations of forest pest population dynamics. A key aspect of this tool will be feedback between the pest and its hosts, allowing forest structure (and therefore habitat suitability) to evolve dynamically over time. The software tool will generate maps representing the area and intensity of impact on hosts and graphs describing the uncertainty associated with model output. We will apply efficient, flexible algorithms for population growth and dispersal in complex landscapes that allow processes at different scales in time and space to contribute to pest activity. This technology will make available models of forest pest growth and spread that will be of immediate use to individuals and agencies involved in forest health. The software will allow estimates of future impact from native pests using standardized monitoring data. It will also facilitate estimates of the rate of spread of invasive species. The option of grid-based and metapopulation modeling will encourage model comparison and validation. At present, the greatest limitation in landscape modeling is the availability of accurate and detailed information on landscape structure. However, the number and quality of GIS databases is increasingly rapidly. FHTET, for example, has produced a series of highly detailed risk maps summarizing the habitat suitability of the entire nation?s forests for the pests of greatest concern. As data availability increases, techniques such as we propose to develop that apply population dynamic models in data-rich landscape contexts will give managers unprecedented capability to predict and manage forest pest risks.