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小木虫论坛-学术科研互动平台 » 专业学科区 » 物理 » 理论物理&天文 » 剑桥2012年Modern.Statistical.Methods.for.Astronomy.With.R.Applications
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[资源] 剑桥2012年Modern.Statistical.Methods.for.Astronomy.With.R.Applications

Preface page xv
1 Introduction 1
1.1 The role of statistics in astronomy 1
1.1.1 Astronomy and astrophysics 1
1.1.2 Probability and statistics 3
1.1.3 Statistics and science 4
1.2 History of statistics in astronomy 6
1.2.1 Antiquity through the Renaissance 6
1.2.2 Foundations of statistics in celestial mechanics 7
1.2.3 Statistics in twentieth-century astronomy 8
1.3 Recommended reading 10
2 Probability 13
2.1 Uncertainty in observational science 13
2.2 Outcome spaces and events 14
2.3 Axioms of probability 15
2.4 Conditional probabilities 17
2.4.1 Bayes’ theorem 18
2.4.2 Independent events 19
2.5 Random variables 20
2.5.1 Density and distribution functions 21
2.5.2 Independent and identically distributed r.v.s. 24
2.6 Quantile function 25
2.7 Discrete distributions 26
2.8 Continuous distributions 27
2.9 Distributions that are neither discrete nor continuous 29
2.10 Limit theorems 30
2.11 Recommended reading 30
2.12 R applications 31
3 Statistical inference 35
3.1 The astronomical context 35
3.2 Concepts of statistical inference 36
3.3 Principles of point estimation 38
vii
viii Contents
3.4 Techniques of point estimation 40
3.4.1 Method of moments 41
3.4.2 Method of least squares 42
3.4.3 Maximum likelihood method 43
3.4.4 Confidence intervals 45
3.4.5 Calculating MLEs with the EM algorithm 47
3.5 Hypothesis testing techniques 48
3.6 Resampling methods 52
3.6.1 Jackknife 52
3.6.2 Bootstrap 54
3.7 Model selection and goodness-of-fit 57
3.7.1 Nonparametric methods for goodness-of-fit 58
3.7.2 Likelihood-based methods for model selection 60
3.7.3 Information criteria for model selection 61
3.7.4 Comparing different model families 62
3.8 Bayesian statistical inference 63
3.8.1 Inference for the binomial proportion 64
3.8.2 Prior distributions 65
3.8.3 Inference for Gaussian distributions 67
3.8.4 Hypotheses testing and the Bayes factor 69
3.8.5 Model selection and averaging 70
3.8.6 Bayesian computation 71
3.9 Remarks 72
3.10 Recommended reading 73
3.11 R applications 74
4 Probability distribution functions 76
4.1 Binomial and multinomial 76
4.1.1 Ratio of binomial random variables 79
4.2 Poisson 80
4.2.1 Astronomical context 80
4.2.2 Mathematical properties 81
4.2.3 Poisson processes 83
4.3 Normal and lognormal 85
4.4 Pareto (power-law) 87
4.4.1 Least-squares estimation 89
4.4.2 Maximum likelihood estimation 90
4.4.3 Extensions of the power-law 91
4.4.4 Multivariate Pareto 92
4.4.5 Origins of power-laws 93
4.5 Gamma 94
4.6 Recommended reading 96
4.7 R applications 96
4.7.1 Comparing Pareto distribution estimators 97
ix Contents
4.7.2 Fitting distributions to data 101
4.7.3 Scope of distributions in R and CRAN 103
5 Nonparametric statistics 105
5.1 The astronomical context 105
5.2 Concepts of nonparametric inference 106
5.3 Univariate problems 107
5.3.1 Kolmogorov–Smirnov and other e.d.f. tests 107
5.3.2 Robust statistics of location 110
5.3.3 Robust statistics of spread 111
5.4 Hypothesis testing 111
5.4.1 Sign test 112
5.4.2 Two-sample and k-sample tests 112
5.5 Contingency tables 113
5.6 Bivariate and multivariate tests 115
5.7 Remarks 116
5.8 Recommended reading 117
5.9 R applications 117
5.9.1 Exploratory plots and summary statistics 117
5.9.2 Empirical distribution and quantile functions 121
5.9.3 Two-sample tests 124
5.9.4 Contingency tables 125
5.9.5 Scope of nonparametrics in R and CRAN 127
6 Data smoothing: density estimation 128
6.1 The astronomical context 128
6.2 Concepts of density estimation 128
6.3 Histograms 129
6.4 Kernel density estimators 131
6.4.1 Basic properties 131
6.4.2 Choosing bandwidths by cross-validation 132
6.4.3 Multivariate kernel density estimation 133
6.4.4 Smoothing with measurement errors 134
6.5 Adaptive smoothing 134
6.5.1 Adaptive kernel estimators 134
6.5.2 Nearest-neighbor estimators 135
6.6 Nonparametric regression 136
6.6.1 Nadaraya–Watson estimator 136
6.6.2 Local regression 137
6.7 Remarks 138
6.8 Recommended reading 138
6.9 R applications 139
6.9.1 Histogram, quantile function and measurement errors 139
6.9.2 Kernel smoothers 140
x Contents
6.9.3 Nonparametric regressions 144
6.9.4 Scope of smoothing in R and CRAN 148
7 Regression 150
7.1 Astronomical context 150
7.2 Concepts of regression 151
7.3 Least-squares linear regression 154
7.3.1 Ordinary least squares 154
7.3.2 Symmetric least-squares regression 155
7.3.3 Bootstrap error analysis 156
7.3.4 Robust regression 158
7.3.5 Quantile regression 160
7.3.6 Maximum likelihood estimation 161
7.4 Weighted least squares 162
7.5 Measurement error models 164
7.5.1 Least-squares estimators 166
7.5.2 SIMEX algorithm 168
7.5.3 Likelihood-based estimators 169
7.6 Nonlinear models 169
7.6.1 Poisson regression 170
7.6.2 Logistic regression 171
7.7 Model validation, selection and misspecification 172
7.7.1 Residual analysis 173
7.7.2 Cross-validation and the bootstrap 175
7.8 Remarks 176
7.9 Recommended reading 177
7.10 R applications 177
7.10.1 Linear modeling 179
7.10.2 Generalized linear modeling 181
7.10.3 Robust regression 182
7.10.4 Quantile regression 183
7.10.5 Nonlinear regression of galaxy surface brightness profiles 184
7.10.6 Scope of regression in R and CRAN 189
8 Multivariate analysis 190
8.1 The astronomical context 190
8.2 Concepts of multivariate analysis 191
8.2.1 Multivariate distances 192
8.2.2 Multivariate normal distribution 194
8.3 Hypothesis tests 195
8.4 Relationships among the variables 197
8.4.1 Multiple linear regression 197
8.4.2 Principal components analysis 199
8.4.3 Factor and canonical correlation analysis 200
xi Contents
8.4.4 Outliers and robust methods 201
8.4.5 Nonlinear methods 202
8.5 Multivariate visualization 203
8.6 Remarks 204
8.7 Recommended reading 205
8.8 R applications 206
8.8.1 Univariate tests of normality 206
8.8.2 Preparing the dataset 208
8.8.3 Bivariate relationships 209
8.8.4 Principal components analysis 212
8.8.5 Multiple regression and MARS 214
8.8.6 Multivariate visualization 216
8.8.7 Interactive graphical displays 217
8.8.8 Scope of multivariate analysis R and CRAN 220
9 Clustering, classification and data mining 222
9.1 The astronomical context 222
9.2 Concepts of clustering and classification 224
9.2.1 Definitions and scopes 224
9.2.2 Metrics, group centers and misclassifications 225
9.3 Clustering 226
9.3.1 Agglomerative hierarchical clustering 226
9.3.2 k-means and related nonhierarchical partitioning 228
9.4 Clusters with substructure or noise 229
9.5 Mixture models 231
9.6 Supervised classification 232
9.6.1 Multivariate normal clusters 232
9.6.2 Linear discriminant analysis and its generalizations 233
9.6.3 Classification trees 234
9.6.4 Nearest-neighbor classifiers 236
9.6.5 Automated neural networks 237
9.6.6 Classifier validation, improvement and fusion 238
9.7 Remarks 239
9.8 Recommended reading 241
9.9 R applications 242
9.9.1 Unsupervised clustering of COMBO-17 galaxies 242
9.9.2 Mixture models 246
9.9.3 Supervised classification of SDSS point sources 250
9.9.4 LDA, k-nn and ANN classification 251
9.9.5 CART and SVM classification 255
9.9.6 Scope of R and CRAN 259
10 Nondetections: censored and truncated data 261
10.1 The astronomical context 261
xii Contents
10.2 Concepts of survival analysis 263
10.3 Univariate datasets with censoring 266
10.3.1 Parametric estimation 266
10.3.2 Kaplan–Meier nonparametric estimator 268
10.3.3 Two-sample tests 269
10.4 Multivariate datasets with censoring 271
10.4.1 Correlation coefficients 271
10.4.2 Regression models 272
10.5 Truncation 274
10.5.1 Parametric estimation 275
10.5.2 Nonparametric Lynden-Bell–Woodroofe estimator 275
10.6 Remarks 277
10.7 Recommended reading 278
10.8 R applications 279
10.8.1 Kaplan–Meier estimator 279
10.8.2 Two-sample tests with censoring 281
10.8.3 Bivariate and multivariate problems with censoring 284
10.8.4 Lynden-Bell–Woodroofe estimator for truncation 287
10.8.5 Scope of censoring and truncation in R and CRAN 290
11 Time series analysis 292
11.1 The astronomical context 292
11.2 Concepts of time series analysis 294
11.3 Time-domain analysis of evenly spaced data 296
11.3.1 Smoothing 296
11.3.2 Autocorrelation and cross-correlation 297
11.3.3 Stochastic autoregressive models 298
11.3.4 Regression for deterministic models 301
11.4 Time-domain analysis of unevenly spaced data 302
11.4.1 Discrete correlation function 302
11.4.2 Structure function 304
11.5 Spectral analysis of evenly spaced data 304
11.5.1 Fourier power spectrum 305
11.5.2 Improving the periodogram 307
11.6 Spectral analysis of unevenly spaced data 308
11.6.1 Lomb–Scargle periodogram 308
11.6.2 Non-Fourier periodograms 310
11.6.3 Statistical significance of periodogram peaks 312
11.6.4 Spectral analysis of event data 313
11.6.5 Computational issues 314
11.7 State-space modeling and the Kalman filter 315
11.8 Nonstationary time series 317
11.9 1/ f noise or long-memory processes 319
11.10 Multivariate time series 322
xiii Contents
11.11 Remarks 323
11.12 Recommended reading 324
11.13 R applications 325
11.13.1 Exploratory time series analysis 326
11.13.2 Spectral analysis 329
11.13.3 Modeling as an autoregressive process 330
11.13.4 Modeling as a long-memory process 333
11.13.5 Wavelet analysis 334
11.13.6 Scope of time series analysis in R and CRAN 336
12 Spatial point processes 337
12.1 The astronomical context 337
12.2 Concepts of spatial point processes 338
12.3 Tests of uniformity 340
12.4 Spatial autocorrelation 341
12.4.1 Global measures of spatial autocorrelation 341
12.4.2 Local measures of spatial autocorrelation 343
12.5 Spatial interpolation 344
12.6 Global functions of clustering 346
12.6.1 Cumulative second-moment measures 346
12.6.2 Two-point correlation function 348
12.7 Model-based spatial analysis 351
12.7.1 Models for galaxy clustering 351
12.7.2 Models in geostatistics 353
12.8 Graphical networks and tessellations 354
12.9 Points on a circle or sphere 355
12.10 Remarks 357
12.11 Recommended reading 358
12.12 R applications 359
12.12.1 Characterization of autocorrelation 361
12.12.2 Variogram analysis 362
12.12.3 Characterization of clustering 364
12.12.4 Tessellations 368
12.12.5 Spatial interpolation 370
12.12.6 Spatial regression and modeling 373
12.12.7 Circular and spherical statistics 374
12.12.8 Scope of spatial analysis in R and CRAN 377
Appendix A Notation and acronyms 379
Appendix B Getting started withR 382
B.1 History and scope of R/CRAN 382
B.2 Session environment 382
B.3 R object classes 385
xiv Contents
B.4 Basic operations on classes 386
B.5 Input/output 388
B.6 A sample R session 389
B.7 Interfaces to other programs and languages 394
B.8 Computational efficiency 394
B.9 Learning more about R 397
B.10 Recommended reading 398
Appendix C Astronomical datasets 399
C.1 Asteroids 400
C.2 Protostar populations 402
C.3 Globular cluster magnitudes 403
C.4 Stellar abundances 405
C.5 Galaxy clustering 406
C.6 Hipparcos stars 408
C.7 Globular cluster properties 410
C.8 SDSS quasars 411
C.9 SDSS point sources 413
C.10 Galaxy photometry 419
C.11 Elliptical galaxy profiles 420
C.12 X-ray source variability 421
C.13 Sunspot numbers 422
C.14 Exoplanet orbits 423
C.15 Kepler stellar light curves 425
C.16 Sloan Digital Sky Survey 428
C.17 Fermi gamma-ray light curves 430
C.18 Swift gamma-ray bursts 432
References 434
Subject index 462
R and CRAN commands 470
The color plates are to be found between pages 398 and 399.
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