"Part I reprints and reworks Huygens's On Reckoning in Games of Chance. Part II offers a thorough treatment of the mathematics of combinations and permutations, including the numbers since known as "Bernoulli numbers." In Part III, Bernoulli solves more complicated problems of games of chance using that mathematics. In the final part, Bernoulli's crowning achievement in mathematical probability becomes manifest he applies the mathematics of games of chance to the problems of epistemic probability in civil, moral, and economic matters, proving what we now know as the weak law of large numbers."
An original account of willful ignorance and how this principle relates to modern probability and statistical methods Through a series of colorful stories about great thinkers and the problems they chose to solve, the author traces the historical evolution of probability and explains how statistical methods have helped to propel scientific research. However, the past success of statistics has depended on vast, deliberate simplifications amounting to willful ignorance, and this very success now threatens future advances in medicine, the social sciences, and other fields. Limitations of existing methods result in frequent reversals of scientific findings and recommendations, to the consternation of both scientists and the lay public. Willful Ignorance: The Mismeasure of Uncertainty exposes the fallacy of regarding probability as the full measure of our uncertainty. The book explains how statistical methodology, though enormously productive and influential over the past century, is approaching a crisis. The deep and troubling divide between qualitative and quantitative modes of research, and between research and practice, are reflections of this underlying problem. The author outlines a path toward the re-engineering of data analysis to help close these gaps and accelerate scientific discovery. Willful Ignorance: The Mismeasure of Uncertainty presents essential information and novel ideas that should be of interest to anyone concerned about the future of scientific research. The book is especially pertinent for professionals in statistics and related fields, including practicing and research clinicians, biomedical and social science researchers, business leaders, and policy-makers.
This invaluable and timely book provides a comprehensive “Conflict Prevention and Friction Analysis (CPFA) Model” for researching comparative law in our increasingly technology-led legal and economic order. It provides an in-depth examination of practical case studies, showcasing the real-world application of quantitative methods and theoretical approaches for analysing legal issues.
This book presents an extended dialogue in essay form between specialists in the work of Moses Mendelssohn, and experts in important trends in related late-seventeenth and eighteenth century thought. The first group of contributors explores themes in Mendelssohn’s metaphysics and aesthetics, presenting both their internal argumentative coherence and their historical context. The second outlines the context of Mendelssohn’s views on specific topics, and describes his contribution to the discussion of them. The essays are organized in four sections. The first pairs two essays on Mendelssohn’s theory of language and writing. The second section offers three essays addressing a number of topics in Mathematics and philosophy in Mendelssohn. A group of eight essays follows, dealing with Metaphysics in a historical context. The fourth section presents five essays discussing Mendelssohn’s Aesthetics in a historical context. Moses Mendelssohn’s Metaphysics and Aesthetics arises from a conference held in Amsterdam in 2009, which gathered numerous authorities to address the central theme. Taken together, these eighteen essays present a sophisticated portrait of Mendelssohn, packed with detail and rich in complexity.
In the sixteenth and seventeenth centuries, gamblers and mathematicians transformed the idea of chance from a mystery into the discipline of probability, setting the stage for a series of breakthroughs that enabled or transformed innumerable fields, from gambling, mathematics, statistics, economics, and finance to physics and computer science. This book tells the story of ten great ideas about chance and the thinkers who developed them, tracing the philosophical implications of these ideas as well as their mathematical impact.
A unique book about the relations of computation to its mathematical basics and application models. The evolutionary interpretation of these developments creates a novel understanding of compulational design and control processes The analysis focuses on the pitfalls of transformations from the verbal-physical problem formulation to the final execution activities via mathematical modeling and programming. The book is enlightened with witty cartoons, and is based on a general under graduate level knowledge for anybody interested in the subject. An appropriate course material for introduction to philosphy of science, especially epistemology.
Intended for juniors and seniors majoring in mathematics, as well as anyone pursuing independent study, this book traces the historical development of four different mathematical concepts by presenting readers with the original sources. Each chapter showcases a masterpiece of mathematical achievement, anchored to a sequence of selected primary sources. The authors examine the interplay between the discrete and continuous, with a focus on sums of powers. They then delineate the development of algorithms by Newton, Simpson and Smale. Next they explore our modern understanding of curvature, and finally they look at the properties of prime numbers. The book includes exercises, numerous photographs, and an annotated bibliography.
This book commemorates the scientific contributions of distinguished statistician, Andrei Yakovlev. It reflects upon Dr. Yakovlev’s many research interests including stochastic modeling and the analysis of micro-array data, and throughout the book it emphasizes applications of the theory in biology, medicine and public health. The contributions to this volume are divided into two parts. Part A consists of original research articles, which can be roughly grouped into four thematic areas: (i) branching processes, especially as models for cell kinetics, (ii) multiple testing issues as they arise in the analysis of biologic data, (iii) applications of mathematical models and of new inferential techniques in epidemiology, and (iv) contributions to statistical methodology, with an emphasis on the modeling and analysis of survival time data. Part B consists of methodological research reported as a short communication, ending with some personal reflections on research fields associated with Andrei and on his approach to science. The Appendix contains an abbreviated vitae and a list of Andrei’s publications, complete as far as we know. The contributions in this book are written by Dr. Yakovlev’s collaborators and notable statisticians including former presidents of the Institute of Mathematical Statistics and of the Statistics Section of the AAAS. Dr. Yakovlev’s research appeared in four books and almost 200 scientific papers, in mathematics, statistics, biomathematics and biology journals. Ultimately this book offers a tribute to Dr. Yakovlev’s work and recognizes the legacy of his contributions in the biostatistics community.
This is a collection of classic research papers on the Dempster-Shafer theory of belief functions. The book is the authoritative reference in the field of evidential reasoning and an important archival reference in a wide range of areas including uncertainty reasoning in artificial intelligence and decision making in economics, engineering, and management. The book includes a foreword reflecting the development of the theory in the last forty years.
Methodology in research refers to a set of guidelines for designing and carrying out a study. The methodology! is a broad phrase that may refer to several different aspects of a study's execution, including but not limited to its planning, execution, and analysis. The goal of research methodology is to provide answers to a wide range of questions about a research problem or study, such as: why the study was conducted; how the research problem was defined; how and why the hypothesis was formulated; what data were gathered; what method was used to analyze the data; and so on. A researcher will! use a research technique to explain how and why they are doing their study. Study methodology provides the proper setting for the researcher to plot out the study project in context and create sound preparations at the appropriate moment. Moreover, the research technique encourages the researcher to participate actively in the study of his or her chosen topic. In most cases, the study subject and the research purpose will be different from one another, but this may be overcome by using an appropriate approach. In contrast to research methods, which are the particular procedures and instruments used for collecting, analyzing, and interpreting data, research methodology refers to the overarching plan or approach used in conducting a study.
