This volume is concerned with the problems in probability and statistics. Ill-posed problems are usually understood as those results where small changes in the assumptions lead to arbitrarily large changes in the conclusions. Such results are not very useful for practical applications where the presumptions usually hold only approximately (because even a slightest departure from the assumed model may produce an uncontrollable shift in the outcome). Often, the ill-posedness of certain practical problems is due to the lack of their precise mathematical formulation. Consequently, one can deal with such problems by replacing a given ill-posed problem with another, well-posed problem, which in some sense is 'close' to the original one. The goal in this book is to show that ill-posed problems are not just a mere curiosity in the contemporary theory of mathematical statistics and probability. On the contrary, such problems are quite common, and majority of classical results fall into this class. The objective of this book is to identify problems of this type, and re-formulate them more correctly. Thus, alternative (more precise in the above sense) versions are proposed of numerous classical theorems in the theory of probability and mathematical statistics. In addition, some non-standard problems are considered from this point of view.

A Probability Metrics Approach to Financial Risk Measures relates the field of probability metrics and risk measures to one another and applies them to finance for the first time. Helps to answer the question: which risk measure is best for a given problem? Finds new relations between existing classes of risk measures Describes applications in finance and extends them where possible Presents the theory of probability metrics in a more accessible form which would be appropriate for non-specialists in the field Applications include optimal portfolio choice, risk theory, and numerical methods in finance Topics requiring more mathematical rigor and detail are included in technical appendices to chapters

This volume contains a collection of research articles on multivariate statistical methods, encompassing both theoretical advances and emerging applications in a variety of scientific disciplines. It serves as a tribute to Professor S N Roy, an eminent statistician who has made seminal contributions to the area of multivariate statistical methods, on his birth centenary. In the area of emerging applications, the topics include bioinformatics, categorical data and clinical trials, econometrics, longitudinal data analysis, microarray data analysis, sample surveys, statistical process control, etc.Researchers, professionals and advanced graduates will find the book an essential resource for modern developments in theory as well as for innovative and emerging important applications in the area of multivariate statistical methods.

An integrated package of powerful probabilistic tools and key applications in modern mathematical data science.

In 1984, Nam Sub, who was then the Assistant Director for Engineering at the National Science Foundation (NSF), created the Design Theory and Methodology Program. Among his goals in creating this program were to develop a science of engineering design and to establish design as an accepted field of engineering research. From 1984 to 1986 this program was directed by Susan Finger; from 1986 to the present Jack Dixon has been the director. The program itself has covered a broad range of disciplines, from chemical engineering to architecture, and a broad range of research paradigms, from psychological experiments to mathematical models. The present volume is based on the second NSF Grantee Workshop on Design Theory and Methodology, called Design Theory '88, which was held June 2-5, 1988 at Rensselaer Polytechnic Institute in Troy, NY, USA. It is, however, not strictly a proceedings since it includes some material that was not presented at a the Workshop and since it omits some papers and discussions that were presented at the Workshop. At the Workshop, invited speakers presented overviews of six different research areas based on summaries submitted in advance by the grantees of the Design Theory and Methodology Program. Since most of the speakers were not supported under the NSF program they brought fresh views to it. The other papers in this book were submitted directly to this volume and were not presented at the Workshop.

This book studies the problem of the decomposition of a given random variable introduction a sum of independent random variables (components). The central feature of the book is Feldman's use of powerful analytical techniques.

This book studies the problem of the decomposition of a given random variable introduction a sum of independent random variables (components). The central feature of the book is Feldman's use of powerful analytical techniques.

Quantum Inspired Computational Intelligence: Research and Applications explores the latest quantum computational intelligence approaches, initiatives, and applications in computing, engineering, science, and business. The book explores this emerging field of research that applies principles of quantum mechanics to develop more efficient and robust intelligent systems. Conventional computational intelligence—or soft computing—is conjoined with quantum computing to achieve this objective. The models covered can be applied to any endeavor which handles complex and meaningful information. - Brings together quantum computing with computational intelligence to achieve enhanced performance and robust solutions - Includes numerous case studies, tools, and technologies to apply the concepts to real world practice - Provides the missing link between the research and practice