Linked e-resources
Details
Table of Contents
Intro
Preface
How to Use the Text
Contents
About the Authors
1 Probability
1.1 Chance, Chaos and Determinism
1.2 Some Basic Terms
1.3 The Concept of Probability
1.4 Axiomatic Probability
1.5 Repeated Trials
1.6 Elements of Combinatorial Analysis
1.7 Bayes' Theorem
1.8 Learning Algorithms
1.9 Problems
2 Representation of Random Phenomena
2.1 Introduction
2.2 Random Variables
2.3 Cumulative or Distribution Function
2.4 Data Representation
2.5 Discrete Random Variables
2.6 Binomial Distribution
2.7 Continuous Random Variables
3.12 Problems
4 Multivariate Probability Theory
4.1 Introduction
4.2 Multivariate Statistical Distributions
4.3 Covariance and Correlation
4.4 Two-Dimensional Gaussian Distribution
4.5 The General Multidimensional Case
4.6 Multivariate Probability Regions
4.7 Multinomial Distribution
4.8 Problems
5 Functions of Random Variables
5.1 Introduction
5.2 Functions of a Random Variable
5.3 Functions of Several Random Variables
5.4 Mean and Variance Transformation
5.5 Means and Variances for n Variables
5.6 Problems
6 Basic Statistics: Parameter Estimation
6.1 Introduction
6.2 Confidence Intervals
6.3 Confidence Intervals with Pivotal Variables
6.4 Mention of the Bayesian Approach
6.5 Some Notations
6.6 Probability Estimation
6.7 Probability Estimation from Large Samples
6.8 Poissonian Interval Estimation
6.9 Mean Estimation from Large Samples
6.10 Variance Estimation from Large Samples
6.11 Mean and Variance Estimation for Gaussian Samples
6.12 How to Use the Estimation Theory
6.13 Estimates from a Finite Population
6.14 Histogram Analysis
6.15 Estimation of the Correlation
6.16 Problems
7 Basic Statistics: Hypothesis Testing
7.1 Testing One Hypothesis
7.2 The Gaussian z-Test
7.3 Student's t-Test
7.4 Chi-Square Test
7.5 Compatibility Check Between Sample and Population
7.6 Hypothesis Testing with Contingency Tables
7.7 Multiple Tests
7.8 Snedecor's F-Test
7.9 Analysis of Variance (ANOVA)
7.10 Two-Way ANOVA
7.11 Problems
8 Monte Carlo Methods
8.1 Introduction
8.2 What Is Monte Carlo?
8.3 Mathematical Aspects
8.4 Generation of Discrete Random Variables
Preface
How to Use the Text
Contents
About the Authors
1 Probability
1.1 Chance, Chaos and Determinism
1.2 Some Basic Terms
1.3 The Concept of Probability
1.4 Axiomatic Probability
1.5 Repeated Trials
1.6 Elements of Combinatorial Analysis
1.7 Bayes' Theorem
1.8 Learning Algorithms
1.9 Problems
2 Representation of Random Phenomena
2.1 Introduction
2.2 Random Variables
2.3 Cumulative or Distribution Function
2.4 Data Representation
2.5 Discrete Random Variables
2.6 Binomial Distribution
2.7 Continuous Random Variables
3.12 Problems
4 Multivariate Probability Theory
4.1 Introduction
4.2 Multivariate Statistical Distributions
4.3 Covariance and Correlation
4.4 Two-Dimensional Gaussian Distribution
4.5 The General Multidimensional Case
4.6 Multivariate Probability Regions
4.7 Multinomial Distribution
4.8 Problems
5 Functions of Random Variables
5.1 Introduction
5.2 Functions of a Random Variable
5.3 Functions of Several Random Variables
5.4 Mean and Variance Transformation
5.5 Means and Variances for n Variables
5.6 Problems
6 Basic Statistics: Parameter Estimation
6.1 Introduction
6.2 Confidence Intervals
6.3 Confidence Intervals with Pivotal Variables
6.4 Mention of the Bayesian Approach
6.5 Some Notations
6.6 Probability Estimation
6.7 Probability Estimation from Large Samples
6.8 Poissonian Interval Estimation
6.9 Mean Estimation from Large Samples
6.10 Variance Estimation from Large Samples
6.11 Mean and Variance Estimation for Gaussian Samples
6.12 How to Use the Estimation Theory
6.13 Estimates from a Finite Population
6.14 Histogram Analysis
6.15 Estimation of the Correlation
6.16 Problems
7 Basic Statistics: Hypothesis Testing
7.1 Testing One Hypothesis
7.2 The Gaussian z-Test
7.3 Student's t-Test
7.4 Chi-Square Test
7.5 Compatibility Check Between Sample and Population
7.6 Hypothesis Testing with Contingency Tables
7.7 Multiple Tests
7.8 Snedecor's F-Test
7.9 Analysis of Variance (ANOVA)
7.10 Two-Way ANOVA
7.11 Problems
8 Monte Carlo Methods
8.1 Introduction
8.2 What Is Monte Carlo?
8.3 Mathematical Aspects
8.4 Generation of Discrete Random Variables