Riassunto
Approaching computational statistics through its theoretical aspects can be daunting. Often intimidated or distracted by the theory, researchers and students can lose sight of the actual goals and applications of the subject. What they need are its key concepts, an understanding of its methods, experience with its implementation, and practice with computational software. Focusing on the computational aspects of statistics rather than the theoretical, Computational Statistics Handbook with MATLAB uses a down-to-earth approach that makes statistics accessible to a wide range of users. The authors integrate the use of MATLAB throughout the book, allowing readers to see the actual implementation of algorithms, but also include step-by-step procedures to allow implementation with any suitable software. The book concentrates on the simulation/Monte Carlo point of view, and contains algorithms for exploratory data analysis, modeling, Monte Carlo simulation, pattern recognition, bootstrap, classification, cross-validation methods, probability density estimation, random number generation, and other computational statistics methods. Emphasis on the practical aspects of statistics, details of the latest techniques, and real implementation experience make the Computational Statistics Handbook with MATLAB more than just the first book to use MATLAB to solve computational problems in statistics. It also forms an outstanding, introduction to statistics for anyone in the many disciplines that involve data analysis.
Contenuti
PREFACE
INTRODUTION
What is Computational Statistics?
An Overview of the Book
MATLAB Code
Further Reading
PROBABILITY CONCEPTS
Introduction
Probability
Conditional Probability and Independence
Expectation
Common Distributions
MATLAB Code
Further Reading
Exercises
SAMPLING CONCEPTS
Introduction
Sampling Terminology and Concepts
Sampling Distributions
Parameter Estimation
Empirical Distribution Function
MATLAB Code
Further Reading
Exercises
GENERATING RANDOM VARIABLES
Introduction
General Techniques for Generating Random Variables
Generating Continuous Random Variable
Generating Discrete Random Variables
EXPLORATORY DATA ANALYSIS
Introduction
Exploring Univariate Data
Exploring Bivariate and Trivariate Data
Exploring Multi-Dimensional Data
MONTE CARLO METHODS FOR INFERENTIAL STATISTICS
Introduction
Classical Inferential Statistics
Monte Carlo Methods for Inferential Statistics
Bootstrap Methods
Assessing Estimates of Functions
DATA PARTITIONING
Introduction
Cross-Validation
Jackknife
Better Bootstrap Confidence Intervals
Jackknife-After-Bootstrap
PROBABILITY DENSITY ESTIMATION
Introduction
Histograms
Kernel Density Estimation
Finite Mixtures
Generating Random Variables
STATISTICAL PATTERN RECOGNITION
Introduction
Bayes Classification
Evaluating the Classifier
Classification Trees
Clustering
NONPARAMETRIC REGRESSION
Introduction
Smoothing
Kernel Methods
Regression Trees
MARKOV CHAIN MONTE CARLO METHODS
Introduction
Background
Metropolis-Hastings Algorithms
The Gibbs Sampler
Convergence Monitoring
SPATIAL STATISTICS
Introduction
Visualizing Spatial Point Processes
Exploring First Order and Second Order Properties
Modeling Spatial Point Processes
Simulating Spatial Point Processes
APPENDICES
Introduction to MATLAB
Index of Notation
Projection Pursuit Indexes
MATLAB Code for Trees
List of MATLAB Statistics Toolbox Functions
List of Computational Statistics Toolbox Functions
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