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Statistical Methods for Astronomical Data Analysis 2014 ed. [Kietas viršelis]

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  • Formatas: Hardback, 349 pages, aukštis x plotis: 235x155 mm, weight: 7342 g, 46 Illustrations, color; 18 Illustrations, black and white; XIII, 349 p. 64 illus., 46 illus. in color., 1 Hardback
  • Serija: Springer Series in Astrostatistics 3
  • Išleidimo metai: 02-Oct-2014
  • Leidėjas: Springer-Verlag New York Inc.
  • ISBN-10: 1493915061
  • ISBN-13: 9781493915064
Kitos knygos pagal šią temą:
Statistical Methods for Astronomical Data Analysis 2014 ed.Didesnis paveikslėlis
  • Formatas: Hardback, 349 pages, aukštis x plotis: 235x155 mm, weight: 7342 g, 46 Illustrations, color; 18 Illustrations, black and white; XIII, 349 p. 64 illus., 46 illus. in color., 1 Hardback
  • Serija: Springer Series in Astrostatistics 3
  • Išleidimo metai: 02-Oct-2014
  • Leidėjas: Springer-Verlag New York Inc.
  • ISBN-10: 1493915061
  • ISBN-13: 9781493915064
Kitos knygos pagal šią temą:
Pastovi nuoroda: https://www.kriso.lt/db/9781493915064.html
Raktažodžiai:

This book introduces “Astrostatistics” as a subject in its own right with rewarding examples, including work by the authors with galaxy and Gamma Ray Burst data to engage the reader. This includes a comprehensive blending of Astrophysics and Statistics. The first chapter’s coverage of preliminary concepts and terminologies for astronomical phenomenon will appeal to both Statistics and Astrophysics readers as helpful context. Statistics concepts covered in the book provide a methodological framework. A unique feature is the inclusion of different possible sources of astronomical data, as well as software packages for converting the raw data into appropriate forms for data analysis. Readers can then use the appropriate statistical packages for their particular data analysis needs. The ideas of statistical inference discussed in the book help readers determine how to apply statistical tests. The authors cover different applications of statistical techniques already developed or specifically introduced for astronomical problems, including regression techniques, along with their usefulness for data set problems related to size and dimension. Analysis of missing data is an important part of the book because of its significance for work with astronomical data. Both existing and new techniques related to dimension reduction and clustering are illustrated through examples. There is detailed coverage of applications useful for classification, discrimination, data mining and time series analysis. Later chapters explain simulation techniques useful for the development of physical models where it is difficult or impossible to collect data. Finally, coverage of the many R programs for techniques discussed makes this book a fantastic practical reference. Readers may apply what they learn directly to their data sets in addition to the data sets included by the authors.

1 Introduction to Astrophysics 1(90)
1.1 Light and Radiation
1(6)
1.2 Sources of Radiation
7(1)
1.3 Brightness of Stars
8(7)
1.3.1 Absolute Magnitude and Distance
9(1)
1.3.2 Magnitude—Luminosity Relation
10(1)
1.3.3 Different Photometry Systems
11(1)
1.3.4 Stellar Parallax and Stellar Distances
12(2)
1.3.5 Doppler Shift and Stellar Motions
14(1)
1.4 Spectral Characteristics of Stars
15(2)
1.5 Spectral Features and Saha's Ionization Theory
17(6)
1.6 Celestial Co-ordinate Systems
23(3)
1.7 Hertzsprung—Russel Diagram
26(1)
1.8 Stellar Atmosphere
27(14)
1.9 Stellar Evolution and Connection with H—R Diagram
41(12)
1.10 Variable Stars
53(9)
1.11 Stellar Populations
62(7)
1.11.1 Galactic Clusters
62(1)
1.11.2 Globular Clusters
63(2)
1.11.3 Fragmentation of Molecular Clouds and Initial Mass Function (IMF)
65(4)
1.12 Galaxies
69(10)
1.13 Quasars
79(2)
1.14 Pulsars
81(3)
1.15 Gamma Ray Bursts
84(1)
Appendix
85(2)
Exercise
87(1)
References
88(3)
2 Introduction to Statistics 91(18)
2.1 Introduction
91(1)
2.2 Variable
92(1)
2.2.1 Discrete-Continuous
92(1)
2.2.2 Qualitative—Quantitative
92(1)
2.2.3 Cause and Effects
93(1)
2.3 Frequency Distribution
93(2)
2.3.1 Central Tendency
93(1)
2.3.2 Dispersion
94(1)
2.3.3 Skewness
94(1)
2.3.4 Kurtosis
95(1)
2.4 Exploratory Data Analysis
95(2)
2.4.1 Histogram
96(1)
2.4.2 Box Plot
96(1)
2.5 Correlation
97(2)
2.5.1 Scatter Plot
98(1)
2.6 Regression
99(3)
2.7 Multiple Correlation
102(1)
2.8 Random Variable
102(7)
2.8.1 Some Important Discrete Distribution
103(4)
2.8.2 Some Important Continuous Distributions
107(2)
3 Sources of Astronomical Data 109(10)
3.1 Introduction
109(1)
3.2 Sloan Digital Sky Survey
109(5)
3.3 Vizier Service
114(1)
3.4 Data on Eclipsing Binary Stars
114(1)
3.5 Extra Galactic Distance Data Base (EDD) (edd.ifa.hawaii.edu/index.html)
115(1)
3.6 Data on Pulsars
115(1)
3.7 Data on Gamma Ray Bursts
115(1)
3.8 Astronomical and Statistical Softwares
116(1)
Exercises
117(2)
4 Statistical Inference 119(18)
4.1 Population and Sample
119(1)
4.2 Parametric Inference
120(4)
4.2.1 Point Estimation
121(2)
4.2.1.1 Unbiasedness
121(1)
4.2.1.2 Efficiency
122(1)
4.2.1.3 Maximum Likelihood Estimator (MLE)
123(1)
4.2.2 Interval Estimation
123(1)
4.3 Testing of Hypothesis
124(4)
4.3.1 p-Value
125(1)
4.3.2 One Sample and Two Sample Tests
126(2)
4.3.3 Common Distribution Test
128(1)
4.4 Empirical Distribution Function
128(2)
4.5 Nonparametric Approaches
130(5)
4.5.1 Kolmogorov—Smirnov One Sample Test
130(1)
4.5.2 Kolmogorov—Smirnov Two Sample Test
131(1)
4.5.3 Shapiro—Wilk Test
132(1)
4.5.4 Wilcoxon Rank-Sum Test
133(1)
4.5.5 Kruskal—Wallis Two Sample Test
134(1)
Reference
135(2)
5 Advanced Regression and Its Applications with Measurement Error 137(18)
5.1 Introduction
137(1)
5.2 Simple Regression
138(1)
5.3 Multiple Regression
138(4)
5.3.1 Estimation of Parameters in Multiple Regression
139(2)
5.3.2 Goodness of Fit
141(1)
5.3.3 Regression Line Through the Origin
142(1)
5.4 Effectiveness of the Fitted Model
142(1)
5.5 Best Subset Selection
143(3)
5.5.1 Forward and Backward Stepwise Regression
144(1)
5.5.2 Ridge Regression
144(1)
5.5.3 Least Absolute Shrinkage and Selection Operator (LASSO)
145(1)
5.5.4 Least Angle Regression (LAR)
145(1)
5.6 Multicollinearity
146(1)
5.7 Regression Problem in Astronomical Research (Mondal et al. 2010)
147(7)
5.7.1 Regression Planes and Symmetric Regression Plane
149(3)
5.7.2 The Symmetric Regression Plane with Intercept
152(2)
References
154(1)
6 Missing Observations and Imputation 155(8)
6.1 Introduction
155(1)
6.2 Missing Data Mechanism
155(1)
6.2.1 Missingness Completely at Random (MCAR)
155(1)
6.2.2 Missingness at Random (MAR)
156(1)
6.2.3 Missingness that Depends on Unobserved Predictors and the Missing Value Itself
156(1)
6.3 Analysis of Data with Missing Values
156(3)
6.3.1 Complete Case Analysis
156(1)
6.3.2 Imputation Methods
157(7)
6.3.2.1 Mean Imputation
157(1)
6.3.2.2 Hot Deck Imputation (Andridge and Little 2010)
157(1)
6.3.2.3 Cold Deck Imputation (Shao 2000)
158(1)
6.3.2.4 Warm Deck Imputation
159(1)
6.4 Likelihood Based Estimation: EM Algorithm
159(2)
6.5 Multiple Imputation
161(1)
References
162(1)
7 Dimension Reduction and Clustering 163(30)
7.1 Introduction
163(1)
7.2 Principal Component Analysis
164(8)
7.2.1 An Example Related to Application of PCA (Babu et al. 2009)
167(5)
7.2.1.1 The Correlation Vector Diagram (Biplot)
169(3)
7.3 Independent Component Analysis
172(10)
7.3.1 ICA by Maximization of Non-Gaussianity
175(1)
7.3.2 Approximation of Negentropy
176(1)
7.3.3 The FastICA Algorithm
176(1)
7.3.4 ICA Versus PCA
177(2)
7.3.5 An Example (Chattopadhyay et al. 2013)
179(3)
7.4 Factor Analysis
182(8)
7.4.1 Method of Estimation
185(3)
7.4.2 Factor Rotation
188(2)
References
190(3)
8 Clustering, Classification and Data Mining 193(24)
8.1 Introduction
193(1)
8.2 Hierarchical Cluster Technique
193(3)
8.2.1 Agglomerative Methods
194(1)
8.2.2 Distance Measures
194(1)
8.2.3 Single Linkage Clustering
195(1)
8.2.4 Complete Linkage Clustering
195(1)
8.2.5 Average Linkage Clustering
196(1)
8.3 Partitioning Clustering: k-Means Method
196(1)
8.4 Classification
197(3)
8.5 An Example (Chattopadhyay et al. 2007)
200(7)
8.5.1 Cluster Analysis of BATSE Sample and Discriminant Analysis
201(3)
8.5.2 Cluster Analysis of HETE 2 and Swift Samples
204(3)
8.6 Clustering for Large Data Sets: Data Mining
207(8)
8.6.1 Subspace Clustering
207(2)
8.6.2 Clustering in Arbitrary Subspace Based on Hough Transform: An Application (Chattopadhyay et al. 2013)
209(14)
8.6.2.1 Input Parameters
211(1)
8.6.2.2 Data Set
211(1)
8.6.2.3 Experimental Evaluation
211(1)
8.6.2.4 Properties of the Groups
212(3)
References
215(2)
9 Time Series Analysis 217(24)
9.1 Introduction
217(1)
9.2 Several Components of a Time Series
218(1)
9.3 How to Remove Various Deterministic Components from a Time Series
219(1)
9.4 Stationary Time Series and Its Significance
220(1)
9.5 Autocorrelations and Correlogram
220(1)
9.6 Stochastic Process and Stationary Process
221(2)
9.7 Different Stochastic Process Used for Modelling
223(5)
9.7.1 Linear Stationary Models
223(4)
9.7.2 Linear Non Stationary Model
227(1)
9.8 Fitting Models and Estimation of Parameters
228(2)
9.9 Forecasting
230(2)
9.10 Spectrum and Spectral Analysis
232(3)
9.11 Cross-Correlation Function (Wcross(0))
235(5)
References
240(1)
10 Monte Carlo Simulation 241(36)
10.1 Generation of Random Numbers
242(3)
10.2 Test for Randomness
245(1)
10.3 Generation of Random Numbers from Various Distributions
246(10)
10.4 Monte Carlo Method
256(2)
10.5 Importance Sampling
258(3)
10.6 Markov Chain Monte Carlo (MCMC)
261(1)
10.7 Metropolis—Hastings Method
261(14)
References
275(2)
11 Use of Softwares 277(66)
11.1 Introduction
277(1)
11.2 Preliminaries on R
277(1)
11.3 Advantages of R Programming
278(1)
11.4 How to Get R Under Ubuntu Operating System
279(1)
11.5 Basic Operations
279(13)
11.5.1 Computation
279(1)
11.5.2 Vector Operations
280(1)
11.5.3 Matrix Operations
281(4)
11.5.4 Graphics in "R"
285(7)
11.6 Some Statistical Codes in R
292(49)
Appendix 303 About the Authors
341(2)
Index 343
Professor Tanuka Chattopadhyay is a Professor of Applied Mathematics at the University of Calcutta, India. Her areas of research are Astrophysics and Statistics. Professor Tanuka Chattopadhyay has published more than 25 research papers in national and international peer reviewed journals. She has also published two books on Computer Programming and Astrophysics. Professor Chattopadhyay had visiting appointments at the Pennsylvania State University,USA and Institut de Planétologie et d'Astrophysique de Grenoble, Joseph Fourier University, France. Since 2002 she has been the visiting Associate of Inter University centre for Astronomy and Astrophysics (IUCAA), Pune, India. She is a member of International Astrostatistics Association. She has received Major Research Projects Awards from University Grants Commission (UGC) and Department of Science and Technology (DST), India.

Asis Kumar Chattopadhyay is a Professor of Statistics at the University of Calcutta, India. He also worked as an Associate Professor at the Indian Statistical Institute, Kolkata during the period 2007-2008. Much of the material in the book was developed for class lectures at post graduate level in Applied Multivariate Analysis and Statistical Inference. Professor Chattopadhyay has held visiting appointments at the University of Southern Queensland, Australia and Institut de Planétologie et d'Astrophysique de Grenoble, Joseph Fourier University, France. He has also been selected as Visiting Associate of Inter University Center for Astronomy and Astrophysics (IUCAA), Pune, India since the year 2005. Now he is the coordinator of IUCAA Resource Centre at Calcutta University. Professor Chattopadhyay has published more than 40 research articles National and International peer reviewed journals and two books. Professor Chattopadhyay is a member of International Astrostatistics Association, Calcutta Statistical Association, the Indian Association for Productivity, Qualityand Reliability, Operational Research Society of India and the Indian Association for the study of Population.