Paradoxes are poems of science and philosophy that collectively allow us to address broad multidisciplinary issues within a microcosm. A true paradox is a source of creativity and a concise expression that delivers a profound idea and provokes a wild and endless imagination. The study of paradoxes leads to ultimate clarity and, at the same time, indisputably challenges your mind.
Paradoxes in Scientific Inference analyzes paradoxes from many different perspectives: statistics, mathematics, philosophy, science, artificial intelligence, and more. The book elaborates on findings and reaches new and exciting conclusions. It challenges your knowledge, intuition, and conventional wisdom, compelling you to adjust your way of thinking. Ultimately, you will learn effective scientific inference through studying the paradoxes.
Table of Contents
The Joy of Paradoxes: A Random Walk
Introduction to Paradox
Applications of Paradoxes
Probabilistic and Statistical Paradoxes
Mathematical and Plausible Reasoning
Probability and Randomness
Mathematical Logic and Formal Reasoning
Statistical Measures of Scientific Evidence
Introduction to Statistical Methods
Decision Theory Approach
Controversies in Evidence Measures
Causal Space Theory: Unification of Paradigms
Multiplicity: The Black Hole of Scientific Discovery
Scientific Principles and Inferences
Controversies in Scientific Philosophy
Paradox of a Logical System
Paradox and Game Theory
Paradoxes in Artificial Intelligence
Architecture of Artificial Intelligent Agent
Learning and Teaching
Appendix: Mathematical Notations
A Review and Exercises appear at the end of each chapter.
Mark Chang is vice president of biometrics at AMAG Pharmaceuticals and an adjunct professor at Boston University. Dr. Chang is a co-founder of the International Society for Biopharmaceutical Statistics and an elected fellow of the American Statistical Association. He serves on the editorial boards of several statistical journals and has published five books on biostatistics and clinical trial designs.
"… an excellent book discussing the principles of scientific inference for readers with various backgrounds. Paradoxes are seen sporadically in different occasions; a systematic review in this book may reshape the reader’s brain, as the author warns, and, at the very least, provides a fresh view of scientific philosophy."
—Gang Li, Journal of Biopharmaceutical Statistics, 24, 2014
"This is a very, very entertaining book. It is extremely well written, extremely clear, and very highly recommended."
—Norman R. Draper, International Statistical Review (2013), 81
"… the brisk pace makes the pages turn easily and the book is fun …"
—Sandra Z. Keith, MAA Reviews, April 2013