Statistics and Analysis of Scientific Data

Springer, Nov 8, 2016 - Science - 318 pages

The revised second edition of this textbook provides the reader with a solid foundation in probability theory and statistics as applied to the physical sciences, engineering and related fields. It covers a broad range of numerical and analytical methods that are essential for the correct analysis of scientific data, including probability theory, distribution functions of statistics, fits to two-dimensional data and parameter estimation, Monte Carlo methods and Markov chains.

Features new to this edition include:

• a discussion of statistical techniques employed in business science, such as multiple regression analysis of multivariate datasets.
• a new chapter on the various measures of the mean including logarithmic averages.
• new chapters on systematic errors and intrinsic scatter, and on the fitting of data with bivariate errors.
• a new case study and additional worked examples.
• mathematical derivations and theoretical background material have been appropriately marked, to improve the readability of the text.
• end-of-chapter summary boxes, for easy reference.

As in the first edition, the main pedagogical method is a theory-then-application approach, where 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 material. The level is appropriate for undergraduates and beginning graduate students, and as a reference for the experienced researcher. 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.

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Contents

 1 Theory of Probability 1 2 Random Variables and Their Distributions 16 Binomial Gaussian and Poisson 35 4 Functions of Random Variables and Error Propagation 55 5 Maximum Likelihood and Other Methods to Estimate Variables 84 6 Mean Median and Average Values of Variables 107 7 Hypothesis Testing and Statistics 117 8 Maximum Likelihood Methods for TwoVariable Datasets 147
 11 Systematic Errors and Intrinsic Scatter 195 12 Fitting TwoVariable Datasets with Bivariate Errors 202 13 Model Comparison 211 14 Monte Carlo Methods 225 15 Introduction to Markov Chains 237 16 Monte Carlo Markov Chains 248 Numerical Tables 273 References 310

 9 MultiVariable Regression 165 10 Goodness of Fit and Parameter Uncertainty 176