Statistics Data Mining and Machine Learning in Astronomy

Cover
Title
Copyright
Contents
Preface
I Introduction
	1 About the Book and Supporting Material
		1.1 What Do Data Mining, Machine Learning, and Knowledge Discovery Mean?
		1.2 What is This Book About?
		1.3 An Incomplete Survey of the Relevant Literature
		1.4 Introduction to the Python Language and the Git Code Management Tool
		1.5 Description of Surveys and Data Sets Used in Examples
		1.6 Plotting and Visualizing the Data in This Book
		1.7 How to Efficiently Use This Book
		References
	2 Fast Computation on Massive Data Sets
		2.1 Data Types and Data Management Systems
		2.2 Analysis of Algorithmic Efficiency
		2.3 Seven Types of Computational Problem
		2.4 Seven Strategies for Speeding Things Up
		2.5 Case Studies: Speedup Strategies in Practice
		References
II Statistical Frameworks and Exploratory Data Analysis
	3 Probability and Statistical Distributions
		3.1 Brief Overview of Probability and Random Variables
		3.2 Descriptive Statistics
		3.3 Common Univariate Distribution Functions
		3.4 The Central Limit Theorem
		3.5 Bivariate and Multivariate Distribution Functions
		3.6 Correlation Coefficients
		3.7 Random Number Generation for Arbitrary Distributions
		References
	4 Classical Statistical Inference
		4.1 Classical vs. Bayesian Statistical Inference
		4.2 Maximum Likelihood Estimation (MLE)
		4.3 The goodness of Fit and Model Selection
		4.4 ML Applied to Gaussian Mixtures: The Expectation Maximization Algorithm
		4.5 Confidence Estimates: the Bootstrap and the Jackknife
		4.6 Hypothesis Testing
		4.7 Comparison of Distributions
		4.8 Nonparametric Modeling and Histograms
		4.9 Selection Effects and Luminosity Function Estimation
		4.10 Summary
		References
	5 Bayesian Statistical Inference
		5.1 Introduction to the Bayesian Method
		5.2 Bayesian Priors
		5.3 Bayesian Parameter Uncertainty Quantification
		5.4 Bayesian Model Selection
		5.5 Nonuniform Priors: Eddington, Malmquist, and Lutz–Kelker Biases
		5.6 Simple Examples of Bayesian Analysis: Parameter Estimation
		5.7 Simple Examples of Bayesian Analysis: Model Selection
		5.8 Numerical Methods for Complex Problems (MCMC)
		5.9 Summary of Pros and Cons for Classical and Bayesian methods
		References
III Data Mining and Machine Learning
	6 Searching for Structure in Point Data
		6.1 Nonparametric Density Estimation
		6.2 Nearest-Neighbor Density Estimation
		6.3 Parametric Density Estimation
		6.4 Finding Clusters in Data
		6.5 Correlation Functions
		6.6 Which Density Estimation and Clustering Algorithms Should I Use?
		References
	7 Dimensionality and Its Reduction
		7.1 The Curse of Dimensionality
		7.2 The Data Sets Used in This Chapter
		7.3 Principal Component Analysis
		7.4 Nonnegative Matrix Factorization
		7.5 Manifold Learning
		7.6 Independent Component Analysis and Projection Pursuit
		7.7 Which Dimensionality Reduction Technique Should I Use?
		References
	8 Regression and Model Fitting
		8.1 Formulation of the Regression Problem
		8.2 Regression for Linear Models
		8.3 Regularization and Penalizing the Likelihood
		8.4 Principal Component Regression
		8.5 Kernel Regression
		8.6 Locally Linear Regression
		8.7 Nonlinear Regression
		8.8 Uncertainties in the Data
		8.9 Regression that is Robust to Outliers
		8.10 Gaussian Process Regression
		8.11 Overfitting, Underfitting, and Cross-Validation
		8.12 Which Regression Method Should I Use?
		References
	9 Classification
		9.1 Data Sets Used in This Chapter
		9.2 Assigning Categories: Classification
		9.3 Generative Classification
		9.4 K-Nearest-Neighbor Classifier
		9.5 Discriminative Classification
		9.6 Support Vector Machines
		9.7 Decision Trees
		9.8 Evaluating Classifiers: ROC Curves
		9.9 Which Classifier Should I Use?
		References
	10 Time Series Analysis
		10.1 Main Concepts for Time Series Analysis
		10.2 Modeling Toolkit for Time Series Analysis
		10.3 Analysis of Periodic Time Series
		10.4 Temporally Localized Signals
		10.5 Analysis of Stochastic Processes
		10.6 Which Method Should I Use for Time Series Analysis?
		References
IV Appendices
	A An Introduction to Scientific Computing with Python
		A.1 A Brief History of Python
		A.2 The SciPy Universe
		A.3 Getting Started with Python
		A.4 IPython: The Basics of Interactive Computing
		A.5 Introduction to NumPy
		A.6 Visualization with Matplotlib
		A.7 Overview of Useful NumPy/SciPy Modules
		A.8 Efficient Coding with Python and NumPy
		A.9 Wrapping Existing Code in Python
		A.10 Other Resources
	B AstroML:Machine Learning for Astronomy
		B.1 Introduction
		B.2 Dependencies
		B.3 Tools Included in AstroML v0.1
	C Astronomical Flux Measurements andMagnitudes
		C.1 The Definition of the Specific Flux
		C.2 Wavelength Window Function for Astronomical Measurements
		C.3 The Astronomical Magnitude Systems
	D SQL Query for Downloading SDSS Data
	E Approximating the Fourier Transform with the FFT
		References
Visual Figure Index
Index