Ebook: Statistics and Analysis of Scientific Data
Author: Massimiliano Bonamente (auth.)
- Genre: Mathematics // Mathematicsematical Statistics
- Tags: Statistical Physics Dynamical Systems and Complexity, Probability Theory and Stochastic Processes, Statistical Theory and Methods, Numerical and Computational Physics
- Series: Graduate Texts in Physics
- Year: 2013
- Publisher: Springer-Verlag New York
- Edition: 1
- Language: English
- pdf
Statistics and Analysis of Scientific Data covers the foundations of probability theory and statistics, and a number of numerical and analytical methods that are essential for the present-day analyst of scientific data. Topics covered include probability theory, distribution functions of statistics, fits to two-dimensional datasheets and parameter estimation, Monte Carlo methods and Markov chains. Equal attention is paid to the theory and its practical application, and results from classic experiments in various fields are used to illustrate the importance of statistics in the analysis of scientific data.
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 proactive use of the material for practical applications. 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 students' understanding of the topic.
Statistics and Analysis of Scientific Data covers the foundations of probability theory and statistics, and a number of numerical and analytical methods that are essential for the present-day analyst of scientific data. Topics covered include probability theory, distribution functions of statistics, fits to two-dimensional datasheets and parameter estimation, Monte Carlo methods and Markov chains. Equal attention is paid to the theory and its practical application, and results from classic experiments in various fields are used to illustrate the importance of statistics in the analysis of scientific data.
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 proactive use of the material for practical applications. 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 students' understanding of the topic.
Statistics and Analysis of Scientific Data covers the foundations of probability theory and statistics, and a number of numerical and analytical methods that are essential for the present-day analyst of scientific data. Topics covered include probability theory, distribution functions of statistics, fits to two-dimensional datasheets and parameter estimation, Monte Carlo methods and Markov chains. Equal attention is paid to the theory and its practical application, and results from classic experiments in various fields are used to illustrate the importance of statistics in the analysis of scientific data.
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 proactive use of the material for practical applications. 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 students' understanding of the topic.
Content:
Front Matter....Pages i-xv
Theory of Probability....Pages 1-14
Random Variables and Their Distribution....Pages 15-47
Sum and Functions of Random Variables....Pages 49-75
Estimate of Mean and Variance and Confidence Intervals....Pages 77-99
Distribution Function of Statistics and Hypothesis Testing....Pages 101-123
Maximum Likelihood Fit to a Two-Variable Dataset....Pages 125-141
Goodness of Fit and Parameter Uncertainty....Pages 143-163
Comparison Between Models....Pages 165-176
Monte Carlo Methods....Pages 177-187
Markov Chains and Monte Carlo Markov Chains....Pages 189-219
Back Matter....Pages 221-301