This book focuses on the fundamental principles behind scientific methods. The author uses concrete examples to explain principles. He also uses analogies to connect different methods or problems to arrive at a general principle or common notion. The book explores how the principles of scientific methods are not only applicable to scientific research but also in our daily lives. It shows how the scientific method is used to understand how and why things happen, make predictions, prevent mistakes, and solve problems.
Autorentext
Mark Chang is vice president of biometrics at AMAG Pharmaceuticals and an adjunct professor at Boston University. Dr. Chang is an elected fellow of the American Statistical Association and a co-founder of the International Society for Biopharmaceutical Statistics. He serves on the editorial boards of statistical journals and has published seven books in biostatistics and science, including Paradoxes in Scientific Inference, Modern Issues and Methods in Biostatistics, Adaptive Design Theory and Implementation Using SAS and R, and Monte Carlo Simulation for the Pharmaceutical Industry.
Zusammenfassung
Mathematical Theory of Bayesian Statistics introduces the mathematical foundation of Bayesian inference which is well-known to be more accurate in many real-world problems than the maximum likelihood method. Recent research has uncovered several mathematical laws in Bayesian statistics, by which both the generalization loss and the marginal likelihood are estimated even if the posterior distribution cannot be approximated by any normal distribution. FeaturesExplains Bayesian inference not subjectively but objectively. Provides a mathematical framework for conventional Bayesian theorems.Introduces and proves new theorems. Cross validation and information criteria of Bayesian statistics are studied from the mathematical point of view. Illustrates applications to several statistical problems, for example, model selection, hyperparameter optimization, and hypothesis tests. This book provides basic introductions for students, researchers, and users of Bayesian statistics, as well as applied mathematicians.AuthorSumio Watanabe is a professor of Department of Mathematical and Computing Science at Tokyo Institute of Technology. He studies the relationship between algebraic geometry and mathematical statistics.
Inhalt
Science in Perspective. Formal Reasoning. Experimentation. Scientific Inference. Dynamics of Science. Controversies and Challenges. Case Studies. Bibliography. Index.