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EB

EB

Boca Raton : CRC Press, 2017

1 online zdroj

ISBN 9781315366715 (e-kniha : PDF)

ISBN 9781315323602 (e-kniha : Mobi)

ISBN !9781498797320 (chyb.) (vázáno)

Obsahuje bibliografické odkazy.

001478584

1. Introduction 1 // 1.1 What Is This Book About? 1 // 1.2 Units 3 // 1.3 Physical Constants and Their Uncertainties 5 // 1.4 Dimensionless Quantities 5 // 1.5 Software 6 // 1.6 Topics Covered // Problems // References 8 // 2. Aspects of R 11 // 2.1 Getting R 11 // 2.2 Using R 11 // 2.3 Getting Help 12 // 2.4 Libraries and Packages 13 // 2.5 Variables 13 // 2.6 Vectors 14 // 2.7 Arithmetic 15 // 2.8 Data Frames 16 // 2.9 Exporting Data 17 // 2.10 Importing Data 18 // 2.11 Internal Mathematical Functions 18 // 2.12 Writing Your Own Functions 19 // 2.13 Plotting Mathematical Functions 19 // 2.14 Loops 20 // 2.15 Making Decisions 21 // 2.16 Scripts 23 // 2.17 Reading Data from Websites 25 // 2.18 Matrices and Linear Algebra 25 // 2.19 Some Useful Functions and Operations 28 // 2.19.1 Data Frames 28 // 2.19.2 Vectors 29 // 2.19.3 Probability and Statistics 29 // 2.19.4 Plotting 29 // 2.19.5 Matrices and Linear Algebra 30 // 2.19.6 Data, Functions, Libraries, and Packages 30 // 2.19.7 Various Other Functions and Operations 30 // Problems 30 // References 32 // IN. IN // 3. Statistics 33 // 3.1 Populations and Samples 33 // 3.2 Mean, Median, Standard Deviation, and Variance of a Sample.34 // 3.3 Covariance and Correlation 35 // 3.4 Visualizing Data 36 // 3.4.1 Histograms 36 // 3.4.2 Box Plots 37 // 3.4.3 Plotting Data Sets 39 // 3.4.4 Some Plotting Parameters and Commands 42 // 3.5 Estimating Population Statistics 43 // 3.5.1 Confidence Interval for the Population Mean Using // Student’s t Variables 43 // 3.5.2 Confidence Interval for the Population Variance // Using Chi-Square Variables 44 // 3.5.3 Confidence Interval Interpretation 45 // 3.6 Comparing the Means of Two Samples 46 // 3.7 Testing Data for Normality 47 // 3.8 Outlier Identification 49 // 3.8.1 Modified Thompson x Technique 50 // 3.8.2 Chauvenet’s Criterion 51 // Problems 54 // References 56 //

4. Curve Fits 57 // 4.1 Linear Regression 57 // 4.2 Nonlinear Regression 64 // 4.3 Kernel Smoothing 67 // Problems 71 // References 73 // 5. Uncertainty of a Measured Quantity 75 // 5.1 What Is Uncertainty? 75 // 5.2 Random Variables 75 // 5.3 Measurement Uncertainties 78 // 5.4 Elemental Systematic Errors 82 // 5.4.1 Normal Distributions 83 // 5.4.2 Uniform Distributions 83 // 5.4.3 Triangular Distributions 84 // 5.5 Coverage Factors 85 // Problems 89 // References 90 // 6. Uncertainty of a Result Calculated Using Experimental Data 91 // 6.1 Taylor Series Approach 92 // 6.2 Coverage Factors 99 // 6.3 The Kline-McClintock Equation 102 // 6.4 Balance Checks 103 // Problems 103 // References 105 // 7. Taylor Series Uncertainty of a Linear Regression Curve Fit 107 // 7.1 Curve-Fit Expressions 107 // 7.2 Cases to Consider 110 // 7.2.1 Case 1: No Errors in and No Correlations 110 // 7.2.2 Case 2: Random Errors Only 112 // 7.2.3 Case 3: Random and Systematic Errors 114 // 7.3 General Linear Regression Theory 117 // 7.4 Uncertainties in Regression Coefficients 126 // 7.5 Evaluating Uncertainties with Built-in R Functions 127 // Problems 128 // References 129 // 8. Monte Carlo Methods 131 // 8.1 Overall Monte Carlo Approach 131 // 8.2 Random Number Generation 132 // 8.2.1 Accept/Reject Method 133 // 8.2.2 Inverse-cdf Method 136 // 8.3 Random Sampling 137 // 8.4 Uncertainty of a Measured Variable 138 // 8.5 Bootstrapping with Internal Functions in R 141 // 8.6 Monte Carlo Convergence Criteria 143 // 8.7 Uncertainty of a Result Calculated Using Experimental Data 144 // 8.8 Uncertainty Bands for Linear Regression Curve Fits 149 // 8.9 Uncertainty Bands for a Curve Fit with Kernel Smoothing..152 // Problems 155 // References 157 //

9. The Bayesian Approach 159 // 9.1 Bayes’ Theorem for Probability Density Functions 164 // 9.2 Bayesian Estimation of the Mean and Standard Deviation of a Normal Population 167 // Problems 172 // References 174 // Appendix: Probability Density Functions 175 // Index 191

(OCoLC)993757885