Frontiers In Analysis And Probability

The volume presents extensive research devoted to a broad spectrum of mathematical analysis and probability theory. Subjects discussed in this Work are those treated in the so-called Strasbourg–Zürich Meetings. These meetings occur twice yearly in each of the cities, Strasbourg and Zürich, venues of vibrant mathematical communication and worldwide gatherings. The topical scope of the book includes the study of monochromatic random waves defined for general Riemannian manifolds, notions of entropy related to a compact manifold of negative curvature, interacting electrons in a random background, lp-cohomology (in degree one) of a graph and its connections with other topics, limit operators for circular ensembles, polyharmonic functions for finite graphs and Markov chains, the ETH-Approach to Quantum Mechanics, 2-dimensional quantum Yang–Mills theory, Gibbs measures of nonlinear Schrödinger equations, interfaces in spectral asymptotics and nodal sets. Contributions in this Work are composed by experts from the international community, who have presented the state-of-the-art research in the corresponding problems treated. This volume is expected to be a valuable resource to both graduate students and research mathematicians working in analysis, probability as well as their interconnections and applications.

Research in Bayesian analysis and statistical decision theory is rapidly expanding and diversifying, making it increasingly more difficult for any single researcher to stay up to date on all current research frontiers. This book provides a review of current research challenges and opportunities. While the book can not exhaustively cover all current research areas, it does include some exemplary discussion of most research frontiers. Topics include objective Bayesian inference, shrinkage estimation and other decision based estimation, model selection and testing, nonparametric Bayes, the interface of Bayesian and frequentist inference, data mining and machine learning, methods for categorical and spatio-temporal data analysis and posterior simulation methods. Several major application areas are covered: computer models, Bayesian clinical trial design, epidemiology, phylogenetics, bioinformatics, climate modeling and applications in political science, finance and marketing. As a review of current research in Bayesian analysis the book presents a balance between theory and applications. The lack of a clear demarcation between theoretical and applied research is a reflection of the highly interdisciplinary and often applied nature of research in Bayesian statistics. The book is intended as an update for researchers in Bayesian statistics, including non-statisticians who make use of Bayesian inference to address substantive research questions in other fields. It would also be useful for graduate students and research scholars in statistics or biostatistics who wish to acquaint themselves with current research frontiers.

Next Generation Sequencing (NGS) is the latest high throughput technology to revolutionize genomic research. NGS generates massive genomic datasets that play a key role in the big data phenomenon that surrounds us today. To extract signals from high-dimensional NGS data and make valid statistical inferences and predictions, novel data analytic and statistical techniques are needed. This book contains 20 chapters written by prominent statisticians working with NGS data. The topics range from basic preprocessing and analysis with NGS data to more complex genomic applications such as copy number variation and isoform expression detection. Research statisticians who want to learn about this growing and exciting area will find this book useful. In addition, many chapters from this book could be included in graduate-level classes in statistical bioinformatics for training future biostatisticians who will be expected to deal with genomic data in basic biomedical research, genomic clinical trials and personalized medicine. About the editors: Somnath Datta is Professor and Vice Chair of Bioinformatics and Biostatistics at the University of Louisville. He is Fellow of the American Statistical Association, Fellow of the Institute of Mathematical Statistics and Elected Member of the International Statistical Institute. He has contributed to numerous research areas in Statistics, Biostatistics and Bioinformatics. Dan Nettleton is Professor and Laurence H. Baker Endowed Chair of Biological Statistics in the Department of Statistics at Iowa State University. He is Fellow of the American Statistical Association and has published research on a variety of topics in statistics, biology and bioinformatics.

This work looks at statistics and probablity, focusing on such topics as the use of linear statistical models, Bayesian analysis of variability and the uses of hierachical models

This collection of selected, revised and extended contributions resulted from a Workshop on BSDEs, SPDEs and their Applications that took place in Edinburgh, Scotland, July 2017 and included the 8th World Symposium on BSDEs. The volume addresses recent advances involving backward stochastic differential equations (BSDEs) and stochastic partial differential equations (SPDEs). These equations are of fundamental importance in modelling of biological, physical and economic systems, and underpin many problems in control of random systems, mathematical finance, stochastic filtering and data assimilation. The papers in this volume seek to understand these equations, and to use them to build our understanding in other areas of mathematics. This volume will be of interest to those working at the forefront of modern probability theory, both established researchers and graduate students.

What is the role and meaning of probability in physical theory, in particular in two of the most successful theories of our age, quantum physics and statistical mechanics? Laws once conceived as universal and deterministic, such as Newton‘s laws of motion, or the second law of thermodynamics, are replaced in these theories by inherently probabilistic laws. This collection of essays by some of the world‘s foremost experts presents an in-depth analysis of the meaning of probability in contemporary physics. Among the questions addressed are: How are probabilities defined? Are they objective or subjective? What is their explanatory value? What are the differences between quantum and classical probabilities? The result is an informative and thought-provoking book for the scientifically inquisitive.

Synthetic biology offers powerful remedies for some of the world’s most intractable problems, but these solutions are clouded by uncertainty and risk that few strategies are available to address. The incentives for continued development of this emerging technology are prodigious and obvious, and the public deserves assurances that all potential downsides are duly considered and minimized accordingly. Incorporating social science analysis within the innovation process may impose constraints, but its simultaneous support in making the end products more acceptable to society at large should be considered a worthy trade-off. Contributing authors in this volume represent diverse perspectives related to synthetic biology’s social sciences, and reflect on different areas of risk analysis and governance that have developed for the field. Such perspectives include leading scholarly discussion pertaining to risk assessment, governance, ethics, and communication. The chapters of this volume note that while the first twenty years of synthetic biology development have focused strongly on technological innovation and product development, the next twenty should emphasize the synergy between developers, policymakers, and publics to generate the most beneficial, well governed, and transparent technologies and products possible. Many chapters in this volume provide new data and approaches that demonstrate the feasibility for multi-stakeholder efforts involving policymakers, regulators, industrial developers, workers, experts, and societal representatives to share responsibilities in the production of effective and acceptable governance in the face of uncertain risk probabilities. A full consideration of such perspectives may prevent a world of draconian regulations based on an insufficient or incomplete understanding of the science that underpins synthetic biology, as well as any hesitancy or fear by the public to adopt its eventual products.

This book focuses both on the application of recent developments in mathematics to the formulation of nontrivial theory in the social sciences and on the expansion of the mathematical basis of decision theory to increase that theory's usefulness for policy research.