Paradoxes in Scientific Inference

Chang, the vice president of biometrics at AMAG Pharmaceuticals, offers a comprehensive textbook that may also serve as a reference of paradoxes encountered in scientific and mathematical reasoning. H

A scientific theory is originally based on a particular set of observations. How can it be extended to apply outside this original range of cases? This question, which is fundamental to natural philosophy, is considered in detail in this book, which was originally published in 1931, and first published as this third edition in 1973. Sir Harold begins with the principle that 'it is possible to learn from experience and to make inferences from beyond the data directly known to sensation'. He goes on to analyse this principle, discuss its status and investigate its logical consequences. The result is a book of importance to anyone interested in the foundations of modern scientific method. His thesis provides a consistent account of how the theories proposed by physicists have been derived from, and are supported by, experimental data.

Providing the knowledge and practical experience to begin analysing scientific data, this book is ideal for physical sciences students wishing to improve their data handling skills. The book focuses on explaining and developing the practice and understanding of basic statistical analysis, concentrating on a few core ideas, such as the visual display of information, modelling using the likelihood function, and simulating random data. Key concepts are developed through a combination of graphical explanations, worked examples, example computer code and case studies using real data. Students will develop an understanding of the ideas behind statistical methods and gain experience in applying them in practice. Further resources are available at www.cambridge.org/9781107607590, including data files for the case studies so students can practise analysing data, and exercises to test students' understanding.

Providing the knowledge and practical experience to begin analysing scientific data, this book is ideal for physical sciences students wishing to improve their data handling skills. The book focuses on explaining and developing the practice and understanding of basic statistical analysis, concentrating on a few core ideas, such as the visual display of information, modelling using the likelihood function, and simulating random data. Key concepts are developed through a combination of graphical explanations, worked examples, example computer code and case studies using real data. Students will develop an understanding of the ideas behind statistical methods and gain experience in applying them in practice. Further resources are available at www.cambridge.org/9781107607590, including data files for the case studies so students can practise analysing data, and exercises to test students' understanding.

Bas C. van Fraassen presents an original exploration of how we represent the world. Science represents natural phenomena by means of theories, as well as in many concrete ways by such means as picture

Bas C. van Fraassen presents an original exploration of how we represent the world. Science represents natural phenomena by means of theories, as well as in many concrete ways by such means as picture

Beginning with the famous Olber's paradox, paradoxes such as the missing mass, dark energy, baryon to photon ratio and cosmic zero-point energy are examined in detail. The Heisenberg–Lemaitre's units,

Fay and Brittain present statistical hypothesis testing and compatible confidence intervals, focusing on application and proper interpretation. The emphasis is on equipping applied statisticians with enough tools - and advice on choosing among them - to find reasonable methods for almost any problem and enough theory to tackle new problems by modifying existing methods. After covering the basic mathematical theory and scientific principles, tests and confidence intervals are developed for specific types of data. Essential methods for applications are covered, such as general procedures for creating tests (e.g., likelihood ratio, bootstrap, permutation, testing from models), adjustments for multiple testing, clustering, stratification, causality, censoring, missing data, group sequential tests, and non-inferiority tests. New methods developed by the authors are included throughout, such as melded confidence intervals for comparing two samples and confidence intervals associated with Wil

This textbook for graduate students in statistics, data science, and public health deals with the practical challenges that come with big, complex, and dynamic data. It presents a scientific roadmap t

Since antiquity, opposed concepts such as the One and the Many, the Finite and the Infinite, and the Absolute and the Relative, have been a driving force in philosophical, scientific, and mathematical

In Measuring and Reasoning, Fred L. Bookstein examines the way ordinary arithmetic and numerical patterns are translated into scientific understanding, showing how the process relies on two carefully managed forms of argument: • Abduction: the generation of new hypotheses to accord with findings that were surprising on previous hypotheses, and • Consilience: the confirmation of numerical pattern claims by analogous findings at other levels of measurement. These profound principles include an understanding of the role of arithmetic and, more importantly, of how numerical patterns found in one study can relate to numbers found in others. More than 200 figures and diagrams illuminate the text. The book can be read with profit by any student of the empirical nature or social sciences and by anyone concerned with how scientists persuade those of us who are not scientists why we should credit the most important claims about scientific facts or theories.

For over 30 years, the MaxEnt workshops have explored Bayesian and Maximum Entropymethods in scientific, engineering, and signal processing applications. This proceedings volume covers all aspects of

A discrete-time stationary stochastic process with finite variance is said to have long memory if its autocorrelations tend to zero hyperbolically in the lag, i.e. like a power of the lag, as the lag

This interdisciplinary work is a collection of major essays on reasoning: deductive, inductive, abductive, belief revision, defeasible (non-monotonic), cross cultural, conversational, and argumentative. They are each oriented toward contemporary empirical studies. The book focuses on foundational issues, including paradoxes, fallacies, and debates about the nature of rationality, the traditional modes of reasoning, as well as counterfactual and causal reasoning. It also includes chapters on the interface between reasoning and other forms of thought. In general, this last set of essays represents growth points in reasoning research, drawing connections to pragmatics, cross-cultural studies, emotion and evolution.

This interdisciplinary work is a collection of major essays on reasoning: deductive, inductive, abductive, belief revision, defeasible (non-monotonic), cross cultural, conversational, and argumentative. They are each oriented toward contemporary empirical studies. The book focuses on foundational issues, including paradoxes, fallacies, and debates about the nature of rationality, the traditional modes of reasoning, as well as counterfactual and causal reasoning. It also includes chapters on the interface between reasoning and other forms of thought. In general, this last set of essays represents growth points in reasoning research, drawing connections to pragmatics, cross-cultural studies, emotion and evolution.

This book examines the consequences of misspecifications ranging from the fundamental to the nonexistent for the interpretation of likelihood-based methods of statistical estimation and interference. Professor White first explores the underlying motivation for maximum-likelihood estimation, treats the interpretation of the maximum-likelihood estimator (MLE) for misspecified probability models, and gives the conditions under which parameters of interest can be consistently estimated despite misspecification, and the consequences of misspecification, for hypothesis testing in estimating the asymptotic covariance matrix of the parameters. Although the theory presented in the book is motivated by econometric problems, its applicability is by no means restricted to economics. Subject to defined limitations, the theory applies to any scientific context in which statistical analysis is conducted using approximate models.

This book examines the consequences of misspecifications ranging from the fundamental to the nonexistent for the interpretation of likelihood-based methods of statistical estimation and interference. Professor White first explores the underlying motivation for maximum-likelihood estimation, treats the interpretation of the maximum-likelihood estimator (MLE) for misspecified probability models, and gives the conditions under which parameters of interest can be consistently estimated despite misspecification, and the consequences of misspecification, for hypothesis testing in estimating the asymptotic covariance matrix of the parameters. Although the theory presented in the book is motivated by econometric problems, its applicability is by no means restricted to economics. Subject to defined limitations, the theory applies to any scientific context in which statistical analysis is conducted using approximate models.

All scientific disciplines prize predictive success. Conventional statistical analyses, however, treat prediction as secondary, instead focusing on modeling and hence estimation, testing, and detailed physical interpretation, tackling these tasks before the predictive adequacy of a model is established. This book outlines a fully predictive approach to statistical problems based on studying predictors; the approach does not require predictors correspond to a model although this important special case is included in the general approach. Throughout, the point is to examine predictive performance before considering conventional inference. These ideas are traced through five traditional subfields of statistics, helping readers to refocus and adopt a directly predictive outlook. The book also considers prediction via contemporary 'black box' techniques and emerging data types and methodologies where conventional modeling is so difficult that good prediction is the main criterion available

In the daily news and the scientific literature, we are faced with conflicting claims about the effects caused by some treatments, behaviors, and policies. A daily glass of wine prolongs life, or so w

This book provides readers with a novel perspective on abduction. It starts by discussing the major theories of abduction, with emphasis on the hybrid nature of abduction as both inference and intuiti

The world seems divided to either applaud or fear the rise of China, but this book probes deeper by investigating three aspects of the phenomenon in detail: 1) the institutional dilemmas of the prospe

We live in a new age for statistical inference, where modern scientific technology such as microarrays and fMRI machines routinely produce thousands and sometimes millions of parallel data sets, each with its own estimation or testing problem. Doing thousands of problems at once is more than repeated application of classical methods. Taking an empirical Bayes approach, Bradley Efron, inventor of the bootstrap, shows how information accrues across problems in a way that combines Bayesian and frequentist ideas. Estimation, testing and prediction blend in this framework, producing opportunities for new methodologies of increased power. New difficulties also arise, easily leading to flawed inferences. This book takes a careful look at both the promise and pitfalls of large-scale statistical inference, with particular attention to false discovery rates, the most successful of the new statistical techniques. Emphasis is on the inferential ideas underlying technical developments, illustrated

This book seeks to demystify the re-ascendancy of China as a civilization state. China's politics and society are examined in the light of its living civilization, which is the only one of the ancient

James Allen presents an original and penetrating investigation of the notion of inference from signs, which played a central role in ancient philosophical and scientific method. Allen masters a broad

While heated arguments between practitioners of qualitative and quantitative research have begun to test the very integrity of the social sciences, Gary King, Robert Keohane, and Sidney Verba have pr

This volume focuses on the abuse of statistical inference in scientific and statistical literature, as well as in a variety of other sources, presenting examples of misused statistics to show that man

A. W. F. Edwards is one of the most influential mathematical geneticists in the history of the discipline. One of the last students of R. A. Fisher, Edwards pioneered the statistical analysis of phylogeny in collaboration with L. L. Cavalli-Sforza, and helped establish Fisher's concept of likelihood as a standard of statistical and scientific inference. In this book, edited by philosopher of science Rasmus Grønfeldt Winther, Edwards's key papers are assembled alongside commentaries by leading scientists, discussing Edwards's influence on their own research and on thinking in their field overall. In an extensive interview with Winther, Edwards offers his thoughts on his contributions, their legacy, and the context in which they emerged. This book is a resource both for anyone interested in the history and philosophy of genetics, statistics, and science, and for scientists seeking to develop new algorithmic and statistical methods for understanding the genetic relationships between and a

This book showcases the innovative research of Professor Skovgaard, by providing in one place a selection of his most important and influential papers. Introductions by colleagues set in context the h

Paradoxes and paper-folding, Moebius variations and mnemonics, fallacies, magic squares, topological curiosities, parlor tricks, and games ancient and modern, from Polyominoes, Nim, Hex, and the Tower of Hanoi to four-dimensional ticktacktoe. These mathematical recreations, clearly and cleverly presented by Martin Gardner, delight and perplex while demonstrating principles of logic, probability, geometry, and other fields of mathematics. Hexaflexagons, Probability Paradoxes, and the Tower of Hanoi is the inaugural volume in Martin Gardner's New Mathematical Library. This book of the earliest of Gardner's enormously popular Scientific American columns and puzzles continues to challenge and fascinate readers. Now the author, in consultation with experts, has added updates to all the chapters, including new game variations, mathematical proofs, and other developments and discoveries.

Paradoxes and paper-folding, Moebius variations and mnemonics, fallacies, magic squares, topological curiosities, parlor tricks, and games ancient and modern, from Polyominoes, Nim, Hex, and the Tower of Hanoi to four-dimensional ticktacktoe. These mathematical recreations, clearly and cleverly presented by Martin Gardner, delight and perplex while demonstrating principles of logic, probability, geometry, and other fields of mathematics. Hexaflexagons, Probability Paradoxes, and the Tower of Hanoi is the inaugural volume in Martin Gardner's New Mathematical Library. This book of the earliest of Gardner's enormously popular Scientific American columns and puzzles continues to challenge and fascinate readers. Now the author, in consultation with experts, has added updates to all the chapters, including new game variations, mathematical proofs, and other developments and discoveries.

Do you want easy access to the latest methods in scientific computing? This greatly expanded third edition of Numerical Recipes has it, with wider coverage than ever before, many new, expanded and updated sections, and two completely new chapters. The executable C++ code, now printed in colour for easy reading, adopts an object-oriented style particularly suited to scientific applications. Co-authored by four leading scientists from academia and industry, Numerical Recipes starts with basic mathematics and computer science and proceeds to complete, working routines. The whole book is presented in the informal, easy-to-read style that made earlier editions so popular. Highlights of the new material include: a new chapter on classification and inference, Gaussian mixture models, HMMs, hierarchical clustering, and SVMs; a new chapter on computational geometry, covering KD trees, quad- and octrees, Delaunay triangulation, and algorithms for lines, polygons, triangles, and spheres; interior

An intuitive, yet precise introduction to probability theory, stochastic processes, statistical inference, and probabilistic models used in science, engineering, economics, and related fields. This is

A novel defense of abduction, one of the main forms of nondeductive reasoning.With this book, Igor Douven offers the first comprehensive defense of abduction, a form of nondeductive reasoning. Abductive reasoning, which is guided by explanatory considerations, has been under normative pressure since the advent of Bayesian approaches to rationality. Douven argues that, although it deviates from Bayesian tenets, abduction is nonetheless rational. Drawing on scientific results, in particular those from reasoning research, and using computer simulations, Douven addresses the main critiques of abduction. He shows that versions of abduction can perform better than the currently popular Bayesian approaches―and can even do the sort of heavy lifting that philosophers have hoped it would do. Douven examines abduction in detail, comparing it to other modes of inference, explaining its historical roots, discussing various definitions of abduction given in the philosophical literature, and addres

This book examines the birth of the scientific understanding of motion. It investigates which logical tools and methodological principles had to be in place to give a consistent account of motion, and which mathematical notions were introduced to gain control over conceptual problems of motion. It shows how the idea of motion raised two fundamental problems in the 5th and 4th century BCE: bringing together being and non-being, and bringing together time and space. The first problem leads to the exclusion of motion from the realm of rational investigation in Parmenides, the second to Zeno's paradoxes of motion. Methodological and logical developments reacting to these puzzles are shown to be present implicitly in the atomists, and explicitly in Plato who also employs mathematical structures to make motion intelligible. With Aristotle we finally see the first outline of the fundamental framework with which we conceptualise motion today.

Philosophy of Molecular Medicine: Foundational Issues in Theory and Practice aims at a systematic investigation of a number of foundational issues in the field of molecular medicine. The volume is organized around four broad modules focusing, respectively, on the following key aspects: What are the nature, scope, and limits of molecular medicine? How does it provide explanations? How does it represent and model phenomena of interest? How does it infer new knowledge from data and experiments? The essays collected here, authored by prominent scientists and philosophers of science, focus on a handful of mainstream topics in the philosophical literature, such as causation, explanation, modeling, and scientific inference. These previously unpublished contributions shed new light on these traditional topics by integrating them with problems, methods, and results from three prominent areas of contemporary biomedical science: basic research, translational and clinical research, and clinical pr

This book examines the birth of the scientific understanding of motion. It investigates which logical tools and methodological principles had to be in place to give a consistent account of motion, and which mathematical notions were introduced to gain control over conceptual problems of motion. It shows how the idea of motion raised two fundamental problems in the 5th and 4th century BCE: bringing together being and non-being, and bringing together time and space. The first problem leads to the exclusion of motion from the realm of rational investigation in Parmenides, the second to Zeno's paradoxes of motion. Methodological and logical developments reacting to these puzzles are shown to be present implicitly in the atomists, and explicitly in Plato who also employs mathematical structures to make motion intelligible. With Aristotle we finally see the first outline of the fundamental framework with which we conceptualise motion today.