Statistical Models and Analysis in Auditing: A Study of Statistical Models and Methods for Analyzing Nonstandard Mixtures of Distributions in Auditing - National Research Council (The National Academies Press, 1988)

Probability and Algorithms - National Research Council (The National Academies Press, 1992)
Some of the hardest computational problems have been successfully attacked through the use of probabilistic algorithms, which have an element of randomness to them. Concepts from the field of probability are also increasingly useful in analyzing the performance of algorithms, broadening our understanding beyond that provided by the worst-case or average-case analyses. This book surveys both of these emerging areas on the interface of the mathematical sciences and computer science. It is designed to attract new researchers to this area and provide them with enough background to begin explorations of their own.

U.S. Research Institutes in the Mathematical Sciences: Assessment and Perspectives - National Research Council (The National Academies Press, 1999)
This report is the result of a fast-track study of U.S. mathematical sciences research institutes done in response to a request from the National Science Foundation (NSF). The task of the Committee on U.S. Mathematical Sciences Research Institutes was to address the following three questions: What are the characteristic features of effective mathematical sciences research institutes in the ways that they further mathematical research in the United States, and are there ways that the current configuration can be improved? What kinds of institutes should there be in the United States, and how many does the nation need? How should U.S. mathematical sciences research institutes be configured (with regard to, for example, diversity of operating formats, distribution of mathematical fields, and interinstitute cooperation or coordination) in order to have the nation's mathematical research enterprise continue to be most productive and successful?

Assessing the Reliability of Complex Models: Mathematical and Statistical Foundations of Verification, Validation, and Uncertainty Quantification - National Research Council (The National Academies Press, 2012)
Advances in computing hardware and algorithms have dramatically improved the ability to simulate complex processes computationally. Today's simulation capabilities offer the prospect of addressing questions that in the past could be addressed only by resource-intensive experimentation, if at all. Assessing the Reliability of Complex Models recognizes the ubiquity of uncertainty in computational estimates of reality and the necessity for its quantification. As computational science and engineering have matured, the process of quantifying or bounding uncertainties in a computational estimate of a physical quality of interest has evolved into a small set of interdependent tasks: verification, validation, and uncertainty of quantification (VVUQ). In recognition of the increasing importance of computational simulation and the increasing need to assess uncertainties in computational results, the National Research Council was asked to study the mathematical foundations of VVUQ and to recommend steps that will ultimately lead to improved processes. Assessing the Reliability of Complex Models discusses changes in education of professionals and dissemination of information that should enhance the ability of future VVUQ practitioners to improve and properly apply VVUQ methodologies to difficult problems, enhance the ability of VVUQ customers to understand VVUQ results and use them to make informed decisions, and enhance the ability of all VVUQ stakeholders to communicate with each other. This report is an essential resource for all decision and policy makers in the field, students, stakeholders, UQ experts, and VVUQ educators and practitioners.

Statistical Challenges in Assessing and Fostering the Reproducibility of Scientific Results: Summary of a Workshop - National Academies of Sciences, Engineering,; Medicine (The National Academies Press, 2016)
Questions about the reproducibility of scientific research have been raised in numerous settings and have gained visibility through several high-profile journal and popular press articles. Quantitative issues contributing to reproducibility challenges have been considered (including improper data measurement and analysis, inadequate statistical expertise, and incomplete data, among others), but there is no clear consensus on how best to approach or to minimize these problems. A lack of reproducibility of scientific results has created some distrust in scientific findings among the general public, scientists, funding agencies, and industries. While studies fail for a variety of reasons, many factors contribute to the lack of perfect reproducibility, including insufficient training in experimental design, misaligned incentives for publication and the implications for university tenure, intentional manipulation, poor data management and analysis, and inadequate instances of statistical inference. The workshop summarized in this report was designed not to address the social and experimental challenges but instead to focus on the latter issues of improper data management and analysis, inadequate statistical expertise, incomplete data, and difficulties applying sound statistic inference to the available data. Many efforts have emerged over recent years to draw attention to and improve reproducibility of scientific work. This report uniquely focuses on the statistical perspective of three issues: the extent of reproducibility, the causes of reproducibility failures, and the potential remedies for these failures.

Developing a 21st Century Global Library for Mathematics Research - National Research Council (The National Academies Press, 2014)
Like most areas of scholarship, mathematics is a cumulative discipline: new research is reliant on well-organized and well-curated literature. Because of the precise definitions and structures within mathematics, today's information technologies and machine learning tools provide an opportunity to further organize and enhance discoverability of the mathematics literature in new ways, with the potential to significantly facilitate mathematics research and learning. Opportunities exist to enhance discoverability directly via new technologies and also by using technology to capture important interactions between mathematicians and the literature for later sharing and reuse. Developing a 21st Century Global Library for Mathematics Research discusses how information about what the mathematical literature contains can be formalized and made easier to express, encode, and explore. Many of the tools necessary to make this information system a reality will require much more than indexing and will instead depend on community input paired with machine learning, where mathematicians' expertise can fill the gaps of automatization. This report proposes the establishment of an organization; the development of a set of platforms, tools, and services; the deployment of an ongoing applied research program to complement the development work; and the mobilization and coordination of the mathematical community to take the first steps toward these capabilities. The report recommends building on the extensive work done by many dedicated individuals under the rubric of the World Digital Mathematical Library, as well as many other community initiatives. Developing a 21st Century Global Library for Mathematics envisions a combination of machine learning methods and community-based editorial effort that makes a significantly greater portion of the information and knowledge in the global mathematical corpus available to researchers as linked open data through a central organizational entity-referred to in the report as the Digital Mathematics Library. This report describes how such a library might operate - discussing development and research needs, role in facilitating discover and interaction, and establishing partnerships with publishers.

Spatial Statistics and Digital Image Analysis - National Research Council (The National Academies Press, 1991)
Spatial statistics is one of the most rapidly growing areas of statistics, rife with fascinating research opportunities. Yet many statisticians are unaware of those opportunities, and most students in the United States are never exposed to any course work in spatial statistics. Written to be accessible to the nonspecialist, this volume surveys the applications of spatial statistics to a wide range of areas, including image analysis, geosciences, physical chemistry, and ecology. The book describes the contributions of the mathematical sciences, summarizes the current state of knowledge, and identifies directions for research.

Renewing U.S. Mathematics: A Plan for the 1990s - National Research Council (The National Academies Press, 1990)

Challenges in Machine Generation of Analytic Products from Multi-Source Data: Proceedings of a Workshop - National Academies of Sciences, Engineering,; Medicine (The National Academies Press, 2017)
The Intelligence Community Studies Board of the National Academies of Sciences, Engineering, and Medicine convened a workshop on August 9-10, 2017 to examine challenges in machine generation of analytic products from multi-source data. Workshop speakers and participants discussed research challenges related to machine-based methods for generating analytic products and for automating the evaluation of these products, with special attention to learning from small data, using multi-source data, adversarial learning, and understanding the human-machine relationship. This publication summarizes the presentations and discussions from the workshop.

Applying Big Data to Address the Social Determinants of Health in Oncology: Proceedings of a Workshop - National Academies of Sciences, Engineering,; Medicine (The National Academies Press, 2020)
The National Academies of Sciences, Engineering, and Medicine held the workshop Applying Big Data to Address the Social Determinants of Health in Oncology on October 28201329, 2019, in Washington, DC. This workshop examined social determinants of health (SDOH) in the context of cancer, and considered opportunities to effectively leverage big data to improve health equity and reduce disparities. The workshop featured presentations and discussion by experts in technology, oncology, and SDOH, as well as representatives from government, industry, academia, and health care systems. This publication summarizes the presentations and discussions from the workshop.

Motion, Control, and Geometry: Proceedings of a Symposium - National Research Council
Some of the modem developments described in Motion, Control, and Geometry include the geometric control of robot motion and craft orientation, how high-power precision micromotors are engineered for less invasive surgery and self-focusing lens applications, what a mobile robot on a surface has in common with one moving in three dimensions, and how the motion-control problem is simplified by a coupled oscillator's geometric grouping of degrees of freedom and motion time scales. The four papers in these proceedings provide a view through the scientific portal of today's motion-control geometric research into tomorrow's technology. The mathematics needed to carry out this research is that of modem differential geometry, and the questions raised in the field of motion-control geometry go directly to the research frontier. Geometry is a mathematical area too often neglected nowadays in a student's education. This publication will help adjust the control initially imposed about 2,300 years ago on one kind of \

Frontiers in Massive Data Analysis - National Research Council (The National Academies Press, 2013)
Data mining of massive data sets is transforming the way we think about crisis response, marketing, entertainment, cybersecurity and national intelligence. Collections of documents, images, videos, and networks are being thought of not merely as bit strings to be stored, indexed, and retrieved, but as potential sources of discovery and knowledge, requiring sophisticated analysis techniques that go far beyond classical indexing and keyword counting, aiming to find relational and semantic interpretations of the phenomena underlying the data. Frontiers in Massive Data Analysis examines the frontier of analyzing massive amounts of data, whether in a static database or streaming through a system. Data at that scale–terabytes and petabytes–is increasingly common in science (e.g., particle physics, remote sensing, genomics), Internet commerce, business analytics, national security, communications, and elsewhere. The tools that work to infer knowledge from data at smaller scales do not necessarily work, or work well, at such massive scale. New tools, skills, and approaches are necessary, and this report identifies many of them, plus promising research directions to explore. Frontiers in Massive Data Analysis discusses pitfalls in trying to infer knowledge from massive data, and it characterizes seven major classes of computation that are common in the analysis of massive data. Overall, this report illustrates the cross-disciplinary knowledge–from computer science, statistics, machine learning, and application disciplines–that must be brought to bear to make useful inferences from massive data.

Mathematical Research in Materials Science: Opportunities and Perspectives - National Research Council (The National Academies Press, 1993)
This book describes fruitful past collaborations between the mathematical and materials sciences and indicates future challenges. It seeks both to encourage mathematical sciences research that will complement vital research in materials science and to raise awareness of the value of quantitative methods. The volume encourages both communities to increase cross-disciplinary collaborations, emphasizing that each has much to gain from such an increase, and it presents recommendations for facilitating such work. This book is written for both mathematical and materials science researchers interested in advancing research at this interface; for federal and state agency representatives interested in encouraging such collaborations; and for anyone wanting information on how such cross-disciplinary, collaborative efforts can be accomplished successfully.

Statistical Software Engineering - National Research Council
This book identifies challenges and opportunities in the development and implementation of software that contain significant statistical content. While emphasizing the relevance of using rigorous statistical and probabilistic techniques in software engineering contexts, it presents opportunities for further research in the statistical sciences and their applications to software engineering. It is intended to motivate and attract new researchers from statistics and the mathematical sciences to attack relevant and pressing problems in the software engineering setting. It describes the \

Strengthening the Linkages Between the Sciences and the Mathematical Sciences - National Research Council
Over three hundred years ago, Galileo is reported to have said, \

Massive Data Sets: Proceedings of a Workshop - National Research Council (The National Academies Press, 1996)

Statistical Analysis of Massive Data Streams: Proceedings of a Workshop - National Research Council (The National Academies Press, 2004)
Massive data streams, large quantities of data that arrive continuously, are becoming increasingly commonplace in many areas of science and technology. Consequently development of analytical methods for such streams is of growing importance. To address this issue, the National Security Agency asked the NRC to hold a workshop to explore methods for analysis of streams of data so as to stimulate progress in the field. This report presents the results of that workshop. It provides presentations that focused on five different research areas where massive data streams are present: atmospheric and meteorological data; high-energy physics; integrated data systems; network traffic; and mining commercial data streams. The goals of the report are to improve communication among researchers in the field and to increase relevant statistical science activity.

Mathematical Challenges from Theoretical/Computational Chemistry - National Research Council (The National Academies Press, 1995)
Computational methods are rapidly becoming major tools of theoretical, pharmaceutical, materials, and biological chemists. Accordingly, the mathematical models and numerical analysis that underlie these methods have an increasingly important and direct role to play in the progress of many areas of chemistry. This book explores the research interface between computational chemistry and the mathematical sciences. In language that is aimed at non-specialists, it documents some prominent examples of past successful cross-fertilizations between the fields and explores the mathematical research opportunities in a broad cross-section of chemical research frontiers. It also discusses cultural differences between the two fields and makes recommendations for overcoming those differences and generally promoting this interdisciplinary work.

Impact of Advances in Computing and Communications Technologies on Chemical Science and Technology: Report of a Workshop - National Research Council (The National Academies Press, 1999)
The Chemical Sciences Roundtable provides a forum for discussing chemically related issues affecting government, industry and government. The goal is to strengthen the chemical sciences by foster communication among all the important stakeholders. At a recent Roundtable meeting, information technology was identified as an issue of increasing importance to all sectors of the chemical enterprise. This book is the result of a workshop convened to explore this topic.

Mathematics and 21st Century Biology - National Research Council (The National Academies Press, 2005)
The exponentially increasing amounts of biological data along with comparable advances in computing power are making possible the construction of quantitative, predictive biological systems models. This development could revolutionize those biology-based fields of science. To assist this transformation, the U.S. Department of Energy asked the National Research Council to recommend mathematical research activities to enable more effective use of the large amounts of existing genomic information and the structural and functional genomic information being created. The resulting study is a broad, scientifically based view of the opportunities lying at the mathematical science and biology interface. The book provides a review of past successes, an examination of opportunities at the various levels of biological systems2014 from molecules to ecosystems2014an analysis of cross-cutting themes, and a set of recommendations to advance the mathematics-biology connection that are applicable to all agencies funding research in this area.