Statistics for Imaging, Optics, and Photonics

ISBN-10: 0470509457
ISBN-13: 9780470509456
Edition: 2011
Authors: Peter Bajorski
List price: $145.95
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Description: This important resource bridges the gap between imaging, optics, and photonics, and statistics and data analysis. The text contains a wide range of relevant statistical methods including a review of the fundamentals of statistics and expanding into  More...

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Book details

List price: $145.95
Copyright year: 2011
Publisher: John Wiley & Sons, Incorporated
Publication date: 10/7/2011
Binding: Hardcover
Pages: 408
Size: 6.25" wide x 9.50" long x 1.00" tall
Weight: 1.496
Language: English

This important resource bridges the gap between imaging, optics, and photonics, and statistics and data analysis. The text contains a wide range of relevant statistical methods including a review of the fundamentals of statistics and expanding into multivariate techniques. The techniques are explained in the context of real examples from remote sensing, multispectral and hyperspectral imaging, signal processing, color science, and other related disciplines. The book also emphasizes intuitive and geometric understanding of concepts. The topics that are most relevant to imaging, optics, and photonics applications are covered thoroughly. In addition, supplemental topics are discussed to provide an overview of when and how the methods can be used.

Preface
Introduction
Who Should Read This Book
How This Book is Organized
How to Read This Book and Learn from It
Note for Instructors
Book Web Site
Fundamentals of Statistics
Statistical Thinking
Data Format
Descriptive Statistics
Measures of Location
Measures of Variability
Data Visualization
Dot Plots
Histograms
Box Plots
Scatter Plots
Probability and Probability Distributions
Probability and Its Properties
Probability Distributions
Expected Value and Moments
Joint Distributions and Independence
Covariance and Correlation
Rules of Two and Three Sigma
Sampling Distributions and the Laws of Large Numbers
Skewness and Kurtosis
Statistical Inference
Introduction
Point Estimation of Parameters
Definition and Properties of Estimators
The Method of the Moments and Plug-In Principle
The Maximum Likelihood Estimation
Interval Estimation
Hypothesis Testing
Samples From Two Populations
Probability Plots and Testing for Population Distributions
Probability Plots
Kolmogorov-Smirnov Statistic
Chi-Squared Test
Ryan-Joiner Test for Normality
Outlier Detection
Monte Carlo Simulations
Bootstrap
Statistical Models
Introduction
Regression Models
Simple Linear Regression Model
Residual Analysis
Multiple Linear Regression and Matrix Notation
Geometric Interpretation in an n-Dimensional Space
Statistical Inference in Multiple Linear Regression
Prediction of the Response and Estimation of the Mean Response
More on Checking the Model Assumptions
Other Topics in Regression
Experimental Design and Analysis
Analysis of Designs with Qualitative Factors
Other Topics in Experimental Design
Supplement 4A. Vector and Matrix Algebra
Vectors
Matrices
Eigenvalues and Eigenvectors of Matrices
Spectral Decomposition of Matrices
Positive Definite Matrices
A Square Root Matrix
Supplement 4B. Random Vectors and Matrices
Sphering
Fundamentals of Multivariate Statistics
Introduction
The Multivariate Random Sample
Multivariate Data Visualization
The Geometry of the Sample
The Geometric Interpretation of the Sample Mean
The Geometric Interpretation of the Sample Standard Deviation
The Geometric Interpretation of the Sample Correlation Coefficient
The Generalized Variance
Distances in the p-Dimensional Space
The Multivariate Normal (Gaussian) Distribution
The Definition and Properties of the Multivariate Normal Distribution
Properties of the Mahalanobis Distance
Multivariate Statistical Inference
Introduction
Inferences About a Mean Vector
Testing the Multivariate Population Mean
Interval Estimation for the Multivariate Population Mean
Confidence Regions
Comparing Mean Vectors from Two Populations
Equal Covariance Matrices
Unequal Covariance Matrices and Large Samples
Unequal Covariance Matrices and Samples Sizes Not So Large
Inferences About a Variance-Covariance Matrix
How to Check Multivariate Normality
Principal Component Analysis
Introduction
Definition and Properties of Principal Components
Definition of Principal Components
Finding Principal Components
Interpretation of Principal Component Loadings
Scaling of Variables
Stopping Rules for Principal Component Analysis
Fair-Share Stopping Rules
Large-Gap Stopping Rules
Principal Component Scores
Residual Analysis
Statistical Inference in Principal Component Analysis
Independent and Identically Distributed Observations
Imaging Related Sampling Schemes
Further Reading
Canonical Correlation Analysis
Introduction
Mathematical Formulation
Practical Application
Calculating Variability Explained by Canonical Variables
Canonical Correlation Regression
Further Reading
Cross-Validation
Discrimination and Classification - Supervised Learning
Introduction
Classification for Two Populations
Classification Rules for Multivariate Normal Distributions
Cross-Validation of Classification Rules
Fisher's Discriminant Function
Classification for Several Populations
Gaussian Rules
Fisher's Method
Spatial Smoothing for Classification
Further Reading
Clustering - Unsupervised Learning
Introduction
Similarity and Dissimilarity Measures
Similarity and Dissimilarity Measures for Observations
Similarity and Dissimilarity Measures for Variables and Other Objects
Hierarchical Clustering Methods
Single Linkage Algorithm
Complete Linkage Algorithm
Average Linkage Algorithm
Ward Method
Nonhierarchical Clustering Methods
K-Means Method
Clustering Variables
Further Reading
Probability Distributions
Data Sets
Miscellanea
References
Index

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