دانلود کتاب Data Analysis for Scientists and Engineers

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Contents\nPreface\n1. Probability\n 1.1 The Laws of Probability\n 1.2 Probability Distributions\n 1.2.1 Discrete and Continuous Probability Distributions\n 1.2.2 Cumulative Probability Distribution Function\n 1.2.3 Change of Variables\n 1.3 Characterizations of Probability Distributions\n 1.3.1 Medians, Modes, and Full Width at Half Maximum\n 1.3.2 Moments, Means, and Variances\n 1.3.3 Moment Generating Function and the Characteristic Function\n 1.4 Multivariate Probability Distributions\n 1.4.1 Distributions with Two Independent Variables\n 1.4.2 Covariance\n 1.4.3 Distributions with Many Independent Variables\n2.\r Some Useful Probability Distribution Functions\n 2.1 Combinations and Permutations\n 2.2 Binomial Distribution\n 2.3 Poisson Distribution\n 2.4 Gaussian or Normal Distribution\n 2.4.1 Derivation of the Gaussian Distribution—Central Limit Theorem\n 2.4.2 Summary and Comments on the Central Limit Theorem\n 2.4.3 Mean, Moments, and Variance of the Gaussian Distribution\n 2.5 Multivariate Gaussian Distribution\n 2.6 χ^2 Distribution\n 2.6.1 Derivation of the χ^2 Distribution\n 2.6.2 Mean, Mode, and Variance of the X^2 Distribution\n 2.6.3 X^2 Distribution in the Limit of Large n\n 2.6.4 Reduced X^2\n 2.6.5 X^2 for Correlated Variables\n 2.7 Beta Distribution\n3.\r Random Numbers and Monte Carlo Methods\n 3.1 Introduction\n 3.2 Nonuniform Random Deviates\n 3.2.1 Inverse Cumulative Distribution Function Method\n 3.2.2 Multidimensional Deviates\n 3.2.3 Box-Müller Method for Generating Gaussian Deviates\n 3.2.4 Acceptance-Rejection Algorithm\n 3.2.5 Ratio of Uniforms Method\n 3.2.6 Generating Random Deviates from More Complicated Probability Distributions\n 3.3 Monte Carlo Integration\n 3.4 Markov Chains\n 3.4.1 Stationary, Finite Markov Chains\n 3.4.2 Invariant Probability Distributions\n 3.4.3 Continuous Parameter and Multiparameter Markov Chains\n 3.5 Markov Chain Monte Carlo Sampling\n 3.5.1 Examples of Markov Chain Monte Carlo Calculations\n 3.5.2 Metropolis-Hastings Algorithm\n 3.5.3 Gibbs Sampler\n4. Elementary Frequentist Statistics\n 4.1 Introduction to Frequentist Statistics\n 4.2 Means and Variances for Unweighted Data\n 4.3 Data with Uncorrelated Measurement Errors\n 4.4 Data with Correlated Measurement Errors\n 4.5 Variance of the Variance and Student’s t Distribution\n 4.5.1 Variance of the Variance\n 4.5.2 Student’s t Distribution\n 4.5.3 Summary\n 4.6 Principal Component Analysis\n 4.6.1 Correlation Coefficient\n 4.6.2 Principal Component Analysis\n 4.7 Kolmogorov-Smirnov Test\n 4.7.1 One-Sample K-S Test\n 4.7.2 Two-Sample K-S Test\n5. Linear Least Squares Estimation\n 5.1 Introduction\n 5.2 Likelihood Statistics\n 5.2.1 Likelihood Function\n 5.2.2 Maximum Likelihood Principle\n 5.2.3 Relation to Least Squares and X^2 Minimization\n 5.3 Fits of Polynomials to Data\n 5.3.1 Straight Line Fits\n 5.3.2 Fits with Polynomials of Arbitrary Degree\n 5.3.3 Variances, Covariances, and Biases\n 5.3.4 Monte Carlo Error Analysis\n 5.4 Need for Covariances and Propagation of Errors\n 5.4.1 Need for Covariances\n 5.4.2 Propagation of Errors\n 5.4.3 Monte Carlo Error Propagation\n 5.5 General Linear Least Squares\n 5.5.1 Linear Least Squares with Nonpolynomial Functions\n 5.5.2 Fits with Correlations among the Measurement Errors\n 5.5.3 X^2 Test for Goodness of Fit\n 5.6 Fits with More Than One Dependent Variable\n6.\r Nonlinear Least Squares Estimation\n 6.1 Introduction\n 6.2 Linearization of Nonlinear Fits\n 6.2.1 Data with Uncorrelated Measurement Errors\n 6.2.2 Data with Correlated Measurement Errors\n 6.2.3 Practical Considerations\n 6.3 Other Methods for Minimizing S\n 6.3.1 Grid Mapping\n 6.3.2 Method of Steepest Descent, Newton’s Method, and Marquardt’s Method\n 6.3.3 Simplex Optimization\n 6.3.4 Simulated Annealing\n 6.4 Error Estimation\n 6.4.1 Inversion of the Hessian Matrix\n 6.4.2 Direct Calculation of the Covariance Matrix\n 6.4.3 Summary and the Estimated Covariance Matrix\n 6.5 Confidence Limits\n 6.6 Fits with Errors in Both the Dependent and Independent Variables\n 6.6.1 Data with Uncorrelated Errors\n 6.6.2 Data with Correlated Errors\n7.\r Bayesian Statistics\n 7.1 Introduction to Bayesian Statistics\n 7.2 Single-Parameter Estimation: Means, Modes, and Variances\n 7.2.1 Introduction\n 7.2.2 Gaussian Priors and Likelihood Functions\n 7.2.3 Binomial and Beta Distributions\n 7.2.4 Poisson Distribution and Uniform Priors\n 7.2.5 More about the Prior Probability Distribution\n 7.3 Multiparameter Estimation\n 7.3.1 Formal Description of the Problem\n 7.3.2 Laplace Approximation\n 7.3.3 Gaussian Likelihoods and Priors: Connection to Least Squares\n 7.3.4 Difficult Posterior Distributions: Markov Chain Monte Carlo Sampling\n 7.3.5 Credible Intervals\n 7.4 Hypothesis Testing\n 7.5 Discussion\n 7.5.1 Prior Probability Distribution\n 7.5.2 Likelihood Function\n 7.5.3 Posterior Distribution Function\n 7.5.4 Meaning of Probability\n 7.5.5 Thoughts\n8.\r Introduction to Fourier Analysis\n 8.1 Introduction\n 8.2 Complete Sets of Orthonormal Functions\n 8.3 Fourier Series\n 8.4 Fourier Transform\n 8.4.1 Fourier Transform Pairs\n 8.4.2 Summary of Useful Fourier Transform Pairs\n 8.5 Discrete Fourier Transform\n 8.5.1 Derivation from the Continuous Fourier Transform\n 8.5.2 Derivation from the Orthogonality Relations for Discretely Sampled Sine and Cosine Functions\n 8.5.3 Parseval’s Theorem and the Power Spectrum\n 8.6 Convolution and the Convolution Theorem\n 8.6.1 Convolution\n 8.6.2 Convolution Theorem\n9.\r Analysis of Sequences: Power Spectra and Periodograms\n 9.1 Introduction\n 9.2 Continuous Sequences: Data Windows, Spectral Windows, and Aliasing\n 9.2.1 Data Windows and Spectral Windows\n 9.2.2 Aliasing\n 9.2.3 Arbitrary Data Windows\n 9.3 Discrete Sequences\n 9.3.1 The Need to Oversample Fm\n 9.3.2 Nyquist Frequency\n 9.3.3 Integration Sampling\n 9.4 Effects of Noise\n 9.4.1 Deterministic and Stochastic Processes\n 9.4.2 Power Spectrum of White Noise\n 9.4.3 Deterministic Signals in the Presence of Noise\n 9.4.4 Nonwhite, Non-Gaussian Noise\n 9.5 Sequences with Uneven Spacing\n 9.5.1 Least Squares Periodogram\n 9.5.2 Lomb-Scargle Periodogram\n 9.5.3 Generalized Lomb-Scargle Periodogram\n 9.6 Signals with Variable Periods:The O−C Diagram\n10. Analysis of Sequences: Convolution and Covariance\n 10.1 Convolution Revisited\n 10.1.1 Impulse Response Function\n 10.1.2 Frequency Response Function\n 10.2 Deconvolution and Data Reconstruction\n 10.2.1 Effect of Noise on Deconvolution\n 10.2.2 Wiener Deconvolution\n 10.2.3 Richardson-Lucy Algorithm\n 10.3 Autocovariance Functions\n 10.3.1 Basic Properties of Autocovariance Functions\n 10.3.2 Relation to the Power Spectrum\n 10.3.3 Application to Stochastic Processes\n 10.4 Cross-Covariance Functions\n 10.4.1 Basic Properties of Cross-Covariance Functions\n 10.4.2 Relation to X^2 and to the Cross Spectrum\n 10.4.3 Detection of Pulsed Signals in Noise\nAppendices\n A.\r Some Useful Definite Integrals\n B.\r Method of Lagrange Multipliers\n C.\r Additional Properties of the Gaussian Probability Distribution\n D.\r The n-Dimensional Sphere\n E. Review of Linear Algebra and Matrices\n F.\r Limitof [1+f (x)/n]^n for Large n\n G.\r Green’s Function Solutions for Impulse Response Functions\n H.\r Second-Order Autoregressive Process\nBibliography\nIndex