This book is the third edition of a successful textbook for upper-undergraduate and early graduate students, which offers a solid foundation in probability theory and statistics and their application to physical sciences, engineering, biomedical sciences and related disciplines. It provides broad coverage ranging from conventional textbook content of probability theory, random variables, and their statistics, regression, and parameter estimation, to modern methods including Monte-Carlo Markov chains, resampling methods and low-count statistics.

In addition to minor corrections and adjusting structure of the content, particular features in this new edition include:

• Python codes and machine-readable data for all examples, classic experiments, and exercises, which are now more accessible to students and instructors
• New chapters on low-count statistics including the Poisson-based Cash statistic for regression in the low-count regime,and on contingency tables and diagnostic testing.
• An additional example of classic experiments based on testing data for SARS-COV-2 to demonstrate practical applications of the described statistical methods.
  This edition inherits the main pedagogical method of earlier versionsa theory-then-application approachwhere emphasis is placed first on a sound understanding of the underlying theory of a topic, which becomes the basis for an efficient and practical application of the materials. Basic calculus is used in some of the derivations, and no previous background in probability and statistics is required. The book includes many numerical tables of data as well as exercises and examples to aid the readers' understanding of the topic.

Is a modern textbook of statistics including Monte Carlo Markov chains and low-count statistics Presents many classic experiments and application examples to actual data across broad sciences, and COVID-19 Has new chapters on low-count statistics with applications, from astronomy to scientific polling and medical research Provides new Python scripts and all the data, great resources for related classes Offers a complete manual of solutions

Autorentext
Massimiliano Bonamente is a professor of physics and astronomy at the University of Alabama in Huntsville (UAH), USA. He received his laurea degree cum laude in electrical engineering from the Universita' di Perugia, Italy in 1996, and a Ph.D. degree in physics from UAH in 2000. After postdoctoral work at the Osservatorio Astrofisico di Catania, Italy, and the NASA Marshall Space Flight Center, NASA, and as an assistant research professor at UAH, he began a tenure-track appointment at UAH as an assistant professor in 2007, and has been a full professor of physics and astronomy since 2014. He was selected as an outstanding faculty member in the College of Science at UAH in 2011, where he has taught a variety of courses for undergraduate and graduate students in the areas of general physics, mathematics and statistics, thermodynamics, and astrophysics. His research interests are primarily in high-energy astrophysics, cosmology and applied statistics, and he has published over 80refereed journal articles.

Inhalt

Theory of Probability.- Random Variables and Their Distributions.- Three Fundamental Distributions: Binomial, Gaussian and Poisson.- The Distribution of Functions of Random Variables.- Error Propagation and Simulation of Random Variables.- Maximum Likelihood and Other Methods to Estimate Variables.- Mean, Median and Average Values of Variables.- Hypothesis Testing and Statistics.- Maximumlikelihood Methods for Gaussian Data.- Multivariable Regression and Generalized Linear Models.- Goodness of Fit and Parameter Uncertainty for Gaussian Data.- LowCount Statistics.- Maximumlikelihood Methods for lowcount Statistics.- The linear Correlation Coefficient.- Systematic Errors and Intrinsic Scatter.-Regression with Bivariate Errors.- Model Comparison.- Monte Carlo Methods.- Introduction to Markov Chains.- Monte Carlo Markov Chains.