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E-raamat: Data Analysis for Scientists and Engineers

  • Formaat: 408 pages
  • Ilmumisaeg: 20-Sep-2016
  • Kirjastus: Princeton University Press
  • Keel: eng
  • ISBN-13: 9781400883066
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Data Analysis for Scientists and EngineersSuurem pilt
  • Formaat: 408 pages
  • Ilmumisaeg: 20-Sep-2016
  • Kirjastus: Princeton University Press
  • Keel: eng
  • ISBN-13: 9781400883066
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Data Analysis for Scientists and Engineers is a modern, graduate-level text on data analysis techniques for physical science and engineering students as well as working scientists and engineers. Edward Robinson emphasizes the principles behind various techniques so that practitioners can adapt them to their own problems, or develop new techniques when necessary. Robinson divides the book into three sections. The first section covers basic concepts in probability and includes a chapter on Monte Carlo methods with an extended discussion of Markov chain Monte Carlo sampling. The second section introduces statistics and then develops tools for fitting models to data, comparing and contrasting techniques from both frequentist and Bayesian perspectives. The final section is devoted to methods for analyzing sequences of data, such as correlation functions, periodograms, and image reconstruction. While it goes beyond elementary statistics, the text is self-contained and accessible to readers from a wide variety of backgrounds. Specialized mathematical topics are included in an appendix. Based on a graduate course on data analysis that the author has taught for many years, and couched in the looser, workaday language of scientists and engineers who wrestle directly with data, this book is ideal for courses on data analysis and a valuable resource for students, instructors, and practitioners in the physical sciences and engineering. * In-depth discussion of data analysis for scientists and engineers * Coverage of both frequentist and Bayesian approaches to data analysis * Extensive look at analysis techniques for time-series data and images * Detailed exploration of linear and nonlinear modeling of data * Emphasis on error analysis * Instructor's manual (available only to professors)

Arvustused

"Robinson's text is an excellent overview of modern statistical techniques and is sure to become a definitive reference. He ably and concisely presents all of the necessary foundational mathematics while also providing a thorough description of sophisticated methods used by practicing engineers and scientists. I particularly enjoyed the division of the book into frequentist and Bayesian approaches and Robinson's clear discussion of the relative merits of each method."Jeremy Kasdin, Princeton University "With an accessible and consistent style, Data Analysis for Scientists and Engineers stands out for its depth of materials and pedagogical presentation. Building from simple concepts, the book's mathematical rigor and accuracy are solid and logical. This book is appropriate for senior undergraduates, graduate students at all levels, and practicing scientists."Wade Fisher, Michigan State University

Preface xi
1 Probability
1(21)
1.1 The Laws of Probability
1(4)
1.2 Probability Distributions
5(4)
1.2.1 Discrete and Continuous Probability Distributions
5(3)
1.2.2 Cumulative Probability Distribution Function
8(1)
1.2.3 Change of Variables
8(1)
1.3 Characterizations of Probability Distributions
9(7)
1.3.1 Medians, Modes, and Full Width at Half Maximum
9(1)
1.3.2 Moments, Means, and Variances
10(4)
1.3.3 Moment Generating Function and the Characteristic Function
14(2)
1.4 Multivariate Probability Distributions
16(6)
1.4.1 Distributions with Two Independent Variables
16(1)
1.4.2 Covariance
17(2)
1.4.3 Distributions with Many Independent Variables
19(3)
2 Some Useful Probability Distribution Functions
22(28)
2.1 Combinations and Permutations
22(2)
2.2 Binomial Distribution
24(3)
2.3 Poisson Distribution
27(4)
2.4 Gaussian or Normal Distribution
31(6)
2.4.1 Derivation of the Gaussian Distribution---Central Limit Theorem
31(3)
2.4.2 Summary and Comments on the Central Limit Theorem
34(2)
2.4.3 Mean, Moments, and Variance of the Gaussian Distribution
36(1)
2.5 Multivariate Gaussian Distribution
37(4)
2.6 Χ2 Distribution
41(6)
2.6.1 Derivation of the Χ2 Distribution
41(3)
2.6.2 Mean, Mode, and Variance of the Χ2 Distribution
44(1)
2.6.3 Χ2 Distribution in the Limit of Large n
45(1)
2.6.4 Reduced Χ2
46(1)
2.6.5 Χ2 for Correlated Variables
46(1)
2.7 Beta Distribution
47(3)
3 Random Numbers and Monte Carlo Methods
50(31)
3.1 Introduction
50(1)
3.2 Nonuniform Random Deviates
51(8)
3.2.1 Inverse Cumulative Distribution Function Method
52(1)
3.2.2 Multidimensional Deviates
53(1)
3.2.3 Box-Muller Method for Generating Gaussian Deviates
53(1)
3.2.4 Acceptance-Rejection Algorithm
54(3)
3.2.5 Ratio of Uniforms Method
57(2)
3.2.6 Generating Random Deviates from More Complicated Probability Distributions
59(1)
3.3 Monte Carlo Integration
59(4)
3.4 Markov Chains
63(8)
3.4.1 Stationary, Finite Markov Chains
63(2)
3.4.2 Invariant Probability Distributions
65(3)
3.4.3 Continuous Parameter and Multiparameter Markov Chains
68(3)
3.5 Markov Chain Monte Carlo Sampling
71(10)
3.5.1 Examples of Markov Chain Monte Carlo Calculations
71(1)
3.5.2 Metropolis-Hastings Algorithm
72(5)
3.5.3 Gibbs Sampler
77(4)
4 Elementary Frequentist Statistics
81(30)
4.1 Introduction to Frequentist Statistics
81(1)
4.2 Means and Variances for Unweighted Data
82(4)
4.3 Data with Uncorrelated Measurement Errors
86(5)
4.4 Data with Correlated Measurement Errors
91(4)
4.5 Variance of the Variance and Students t Distribution
95(6)
4.5.1 Variance of the Variance
96(2)
4.5.2 Student's t Distribution
98(2)
4.5.3 Summary
100(1)
4.6 Principal Component Analysis
101(6)
4.6.1 Correlation Coefficient
101(1)
4.6.2 Principal Component Analysis
102(5)
4.7 Kolmogorov-Smirnov Test
107(4)
4.7.1 One-Sample K-S Test
107(2)
4.7.2 Two-Sample K-S Test
109(2)
5 Linear Least Squares Estimation
111(44)
5.1 Introduction
111(1)
5.2 Likelihood Statistics
112(8)
5.2.1 Likelihood Function
112(3)
5.2.2 Maximum Likelihood Principle
115(4)
5.2.3 Relation to Least Squares and Χ2 Minimization
119(1)
5.3 Fits of Polynomials to Data
120(17)
5.3.1 Straight Line Fits
120(6)
5.3.2 Fits with Polynomials of Arbitrary Degree
126(2)
5.3.3 Variances, Covariances, and Biases
128(8)
5.3.4 Monte Carlo Error Analysis
136(1)
5.4 Need for Covariances and Propagation of Errors
137(7)
5.4.1 Need for Covariances
137(2)
5.4.2 Propagation of Errors
139(3)
5.4.3 Monte Carlo Error Propagation
142(2)
5.5 General Linear Least Squares
144(8)
5.5.1 Linear Least Squares with Nonpolynomial Functions
144(3)
5.5.2 Fits with Correlations among the Measurement Errors
147(2)
5.5.3 Χ2 Test for Goodness of Fit
149(3)
5.6 Fits with More Than One Dependent Variable
152(3)
6 Nonlinear Least Squares Estimation
155(32)
6.1 Introduction
155(2)
6.2 Linearization of Nonlinear Fits
157(6)
6.2.1 Data with Uncorrelated Measurement Errors
158(3)
6.2.2 Data with Correlated Measurement Errors
161(1)
6.2.3 Practical Considerations
162(1)
6.3 Other Methods for Minimizing S
163(8)
6.3.1 Grid Mapping
163(1)
6.3.2 Method of Steepest Descent, Newton's Method, and Marquardt's Method
164(4)
6.3.3 Simplex Optimization
168(1)
6.3.4 Simulated Annealing
168(3)
6.4 Error Estimation
171(5)
6.4.1 Inversion of the Hessian Matrix
171(2)
6.4.2 Direct Calculation of the Covariance Matrix
173(3)
6.4.3 Summary and the Estimated Covariance Matrix
176(1)
6.5 Confidence Limits
176(5)
6.6 Fits with Errors in Both the Dependent and Independent Variables
181(6)
6.6.1 Data with Uncorrelated Errors
182(2)
6.6.2 Data with Correlated Errors
184(3)
7 Bayesian Statistics
187(34)
7.1 Introduction to Bayesian Statistics
187(4)
7.2 Single-Parameter Estimation: Means, Modes, and Variances
191(8)
7.2.1 Introduction
191(1)
7.2.2 Gaussian Priors and Likelihood Functions
192(2)
7.2.3 Binomial and Beta Distributions
194(1)
7.2.4 Poisson Distribution and Uniform Priors
195(3)
7.2.5 More about the Prior Probability Distribution
198(1)
7.3 Multiparameter Estimation
199(15)
7.3.1 Formal Description of the Problem
199(1)
7.3.2 Laplace Approximation
200(3)
7.3.3 Gaussian Likelihoods and Priors: Connection to Least Squares
203(8)
7.3.4 Difficult Posterior Distributions: Markov Chain Monte Carlo Sampling
211(1)
7.3.5 Credible Intervals
212(2)
7.4 Hypothesis Testing
214(3)
7.5 Discussion
217(4)
7.5.1 Prior Probability Distribution
217(1)
7.5.2 Likelihood Function
218(1)
7.5.3 Posterior Distribution Function
218(1)
7.5.4 Meaning of Probability
219(1)
7.5.5 Thoughts
219(2)
8 Introduction to Fourier Analysis
221(35)
8.1 Introduction
221(1)
8.2 Complete Sets of Orthonormal Functions
221(5)
8.3 Fourier Series
226(7)
8.4 Fourier Transform
233(9)
8.4.1 Fourier Transform Pairs
234(7)
8.4.2 Summary of Useful Fourier Transform Pairs
241(1)
8.5 Discrete Fourier Transform
242(7)
8.5.1 Derivation from the Continuous Fourier Transform
243(2)
8.5.2 Derivation from the Orthogonality Relations for Discretely Sampled Sine and Cosine Functions
245(3)
8.5.3 Parseval's Theorem and the Power Spectrum
248(1)
8.6 Convolution and the Convolution Theorem
249(7)
8.6.1 Convolution
249(5)
8.6.2 Convolution Theorem
254(2)
9 Analysis of Sequences: Power Spectra and Periodograms
256(36)
9.1 Introduction
256(1)
9.2 Continuous Sequences: Data Windows, Spectral Windows, and Aliasing
256(9)
9.2.1 Data Windows and Spectral Windows
257(6)
9.2.2 Aliasing
263(2)
9.2.3 Arbitrary Data Windows
265(1)
9.3 Discrete Sequences
265(6)
9.3.1 The Need to Oversample Fm
266(1)
9.3.2 Nyquist Frequency
267(3)
9.3.3 Integration Sampling
270(1)
9.4 Effects of Noise
271(7)
9.4.1 Deterministic and Stochastic Processes
271(1)
9.4.2 Power Spectrum of White Noise
272(3)
9.4.3 Deterministic Signals in the Presence of Noise
275(2)
9.4.4 Nonwhite, Non-Gaussian Noise
277(1)
9.5 Sequences with Uneven Spacing
278(9)
9.5.1 Least Squares Periodogram
278(2)
9.5.2 Lomb-Scargle Periodogram
280(4)
9.5.3 Generalized Lomb-Scargle Periodogram
284(3)
9.6 Signals with Variable Periods: The O-C Diagram
287(5)
10 Analysis of Sequences: Convolution and Covariance
292(41)
10.1 Convolution Revisited
292(9)
10.1.1 Impulse Response Function
292(5)
10.1.2 Frequency Response Function
297(4)
10.2 Deconvolution and Data Reconstruction
301(8)
10.2.1 Effect of Noise on Deconvolution
301(4)
10.2.2 Wiener Deconvolution
305(3)
10.2.3 Richardson-Lucy Algorithm
308(1)
10.3 Autocovariance Functions
309(15)
10.3.1 Basic Properties of Autocovariance Functions
309(4)
10.3.2 Relation to the Power Spectrum
313(3)
10.3.3 Application to Stochastic Processes
316(8)
10.4 Cross-Covariance Functions
324(9)
10.4.1 Basic Properties of Cross-Covariance Functions
324(2)
10.4.2 Relation to Χ2 and to the Cross Spectrum
326(3)
10.4.3 Detection of Pulsed Signals in Noise
329(4)
Appendices
A Some Useful Definite Integrals
333(5)
B Method of Lagrange Multipliers
338(4)
C Additional Properties of the Gaussian Probability Distribution
342(10)
D The n-Dimensional Sphere
352(2)
E Review of Linear Algebra and Matrices
354(20)
F Limit of [ 1 + f(x)/n]n for Large n
374(1)
G Greens Function Solutions for Impulse Response Functions
375(4)
H Second-Order Autoregressive Process
379(4)
Bibliography 383(2)
Index 385
Edward L. Robinson is the William B. Blakemore II Regents Professor of Astronomy at the University of Texas, Austin.
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