| Title: | Statistics and Analysis of Scientific Data |
| Authors: | Bonamente, Massimiliano |
| Keywords: | Statistics and Analysis Statistics |
| Issue Date: | 2017 |
| Publisher: | Springer |
| Abstract: | Across all sciences, a quantitative analysis of data is necessary to assess the significance of experiments, observations, and calculations. This book was written over a period of 10 years, as I developed an introductory graduate course on statistics and data analysis at the University of Alabama in Huntsville. My goal was to put together the material that a student needs for the analysis and statistical interpretation of data, including an extensive set of applications and problems that illustrate the practice of statistical data analysis. The literature offers a variety of books on statistical methods and probability theory. Some are primarily on the mathematical foundations of statistics, some are purely on the theory of probability, and others focus on advanced statistical methods for specific sciences. This textbook contains the foundations of probability, statistics, and data analysis methods that are applicable to a variety of fields— from astronomy to biology, business sciences, chemistry, engineering, physics, and more—with equal emphasis on mathematics and applications. The book is therefore not specific to a given discipline, nor does it attempt to describe every possible statistical method. Instead, it focuses on the fundamental methods that are used across the sciences and that are at the basis of more specific techniques that can be found in more specialized textbooks or research articles |
| Description: | This textbook covers probability theory and random variables, maximum- likelihood methods for single variables and two-variable datasets, and more complex topics of data fitting, estimation of parameters, and confidence intervals. Among the topics that have recently become mainstream, Monte Carlo Markov chains occupy a special role. The last chapter of the book provides a comprehensive overview of Markov chains and Monte Carlo Markov chains, from theory to implementation. I believe that a description of the mathematical properties of statistical tests is necessary to understand their applicability. This book therefore contains mathemat- ical derivations that I considered particularly useful for a thorough understanding of the subject; the book refers the reader to other sources in case of mathematics that goes beyond that of basic calculus. The reader who is not familiar with calculus may skip those derivations and continue with the applications. Nonetheless, statistics is necessarily slanted toward applications. To highlight the relevance of the statistical methods described, I have reported original data from four fundamental scientific experiments from the past two centuries: J.J. Thomson’s experiment that led to the discovery of the electron, G. Mendel’s data on plant characteristics that led to the law of independent assortment of species, E. Hubble’s observation of nebulae that uncovered the expansion of the universe, and K. Pearson’s collection of biometric characteristics in the UK in the early twentieth century. These experiments are used throughout the book to illustrate how statistical methods are applied to actual data and are used in several end-of-chapter problems. The reader will therefore have an opportunity to see statistics in action on these classic experiments and several additional examples. The material presented in this book is aimed at upper-level undergraduate students or beginning graduate students. The reader is expected to be familiar with basic calculus, and no prior knowledge of statistics or probability is assumed. Professional scientists and researchers will find it a useful reference for fundamental methods such as maximum-likelihood fit, error propagation formulas, goodness of fit and model comparison, Monte Carlo methods such as the jackknife and bootstrap, Monte Carlo Markov chains, Kolmogorov-Smirnov tests, and more. All subjects are complemented by an extensive set of numerical tables that make the book completely self-contained. The material presented in this book can be comfortably covered in a one-semester course and has several problems at the end of each chapter that are suitable as homework assignments or exam questions. Problems are both of theoretical and numerical nature, so that emphasis is equally placed on conceptual and practical understanding of the subject. Several datasets, including those in the four “classic experiments,” are used across several chapters, and the students can therefore use them in applications of increasing difficulty. |
| URI: | http://localhost:8080/xmlui/handle/123456789/289 |
| ISBN: | 978-1-4939-6572-4 |
| Appears in Collections: | ARTS & SCIENCE |
| File | Description | Size | Format | |
|---|---|---|---|---|
| 2017_Book_StatisticsAndAnalysisOfScienti.pdf | 5.74 MB | Adobe PDF | View/Open |
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