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This book presents in a compact form the program carried out in introductory statistics courses and discusses some essential topics for research activity, such as Monte Carlo simulation techniques, methods of statistical inference, best fit and analysis of laboratory data. All themes are developed starting from fundamentals, highlighting their applicative aspects, up to the detailed description of several cases particularly relevant for technical and scientific research. The text is dedicated to university students in scientific fields and to all researchers who have to solve practical problems by applying data analysis and simulation procedures. The R software is adopted throughout the book, with a rich library of original programs accessible to the readers through a website.
This book is aimed primarily at students of scientific undergraduate courses, such as engineering, computer science, and physics. However, we think that it can also be useful to all those scientific researchers who have to solve practical problems involving probabilistic, statistical, and simulation aspects. For this reason, we have given space to some topics, such as Monte Carlo methods and their applications, minimization techniques, and data analysis methods, which, usually, are only briefly mentioned in introductory texts.
The mathematical knowledge required by the reader is that which is normally given in the teaching of the basic calculus course in the scientific degrees, with the addition of minimum notions of linear algebra and advanced calculus, such as the elementary concepts of the derivation and integration of multidimensional functions.
This book makes use of the statistical software R, which has now become the world standard for solving statistical problems. The 2019 ranking of the Institute of American Electrical and Electronic Engineers (IEEE) places R in fourth position among the most popular programming languages, after Python, Java, and C. Many R routines have been written by us, to guide the reader while going through the text. These routines can be easily downloaded from the link specified below. We therefore recommend an interactive reading, in which the study of a topic is followed by the use of R routines in the way showed both in the text and in the technical instructions included in the indicated Web pages.
Probability
Representation of Random Phenomena
Basic Probability Theory
Multivariate Probability Theory
Functions of Random Variables
Basic Statistics: Parameter Estimation
Basic Statistics: Hypothesis Testing
Monte Carlo Methods
Applications of Monte Carlo Methods
Statistical Inference and Likelihood
Least Squares
Experimental Data Analysis
A Table of Symbols
B R Software C Moment-Generating Functions
D Solutions of Problems
E Tables