This book covers methods for evaluation of experimental data commonly encountered in science and engineering. Measurements of quantities that vary in a continuous fashion, cannot be measured exactly; it is of interest to be able to quantify these uncertainties. The book centers around using the (free) software package R.
This book covers methods for evaluation of experimental data commonly encountered in science and engineering. Measurements of quantities that vary in a continuous fashion, cannot be measured exactly; it is of interest to be able to quantify these uncertainties. The book centers around using the (free) software package R.Hinweis: Dieser Artikel kann nur an eine deutsche Lieferadresse ausgeliefert werden.
Benjamin D. Shaw is a professor in the Mechanical and Aerospace Engineering Department at the University of California, Davis. His research interests are primarily in experimental and theoretical aspects of combustion. Along with other courses, he has taught undergraduate and graduate courses on engineering experimentation and uncertainty analysis. He has published widely in archival journals and became an ASME Fellow in 2003.
Inhaltsangabe
CHAPTER 1 INTRODUCTION What Is This Book About? Units Physical Constants and Their Uncertainties Dimensionless Quantities Software CHAPTER 2 ASPECTS OF R * Getting R Using R Getting Help Libraries and Packages Variables Vectors Arithmetic Data Frames Exporting Data Importing Data Internal Mathematical Functions Writing Your Own Functions Plotting Mathematical Functions Loops Making Decisions Scripts Reading Data from Websites Matrices and Linear Algebra Some Useful Functions and Operations CHAPTER 3 STATISTICS * Populations and Samples Mean Median Standard Deviation and Variance of a Sample Covariance and Correlation Visualizing Data Histograms Box Plots Plotting Data Sets Some Plotting Parameters and Commands Estimating Population Statistics Confidence Interval for the Population Mean Using Student's t Variables Confidence Interval for the Population Variance Using Chi-Square Variables Confidence Interval Interpretation Comparing the Means of Two Samples Testing Data for Normality Outlier Identification Modified Thompson Technique Chauvenet's Criterion * CHAPTER 4 CURVE FITS * Linear Regression Nonlinear Regression Kernel Smoothing CHAPTER 5 UNCERTAINTY OF A MEASURED QUANTITY * What Is Uncertainty? Random Variables Measurement Uncertainties Elemental Systematic Errors Normal Distributions Uniform Distributions Triangular Distributions CHAPTER 6 UNCERTAINTY OF A RESULT CALCULATED USING EXPERIMENTAL DATA * Taylor Series Approach. Coverage Factors The Kline-McClintock Equation Balance Checks CHAPTER 7 TAYLOR SERIES UNCERTAINTY OF A LINEAR REGRESSION CURVE FIT Curve-fit Expressions Cases to Consider: Case 1: No Errors and No Correlations Case 2: Random Errors Only Case 3: Random and Systematic Errors * General Linear Regression Theory Uncertainties in Regression Coefficients Evaluating Uncertainties with Built-in R functions * CHAPTER 8 MONTE CARLO METHODS * Overall Monte Carlo Approach Random Number Generation Accept/Reject Method Inverse-cdf Method *Random Sampling Uncertainty of a Measured Variable Bootstrapping with Internal Functions in R Monte Carlo Convergence Criteria Uncertainty of a Result Calculated Using Experimental Data Uncertainty Bands for Linear Regression Curve Fits Uncertainty Bands for a Curve Fit with Kernel Smoothing * CHAPTER 9 THE BAYESIAN APPROACH * Bayes Theorem for Probability Density Functions; Bayesian Estimation of the Mean and Standard Deviation of a Normal Population * APPENDIX PROBABILITY DENSITY FUNCTIONS * Univariate pdfs Normal Distribution Uniform Distribution Triangular Distribution Student's t Distribution Chi-Square Distribution Multivariate pdfs Marginal Distributions References *
CHAPTER 1 INTRODUCTION What Is This Book About? Units Physical Constants and Their Uncertainties Dimensionless Quantities Software CHAPTER 2 ASPECTS OF R * Getting R Using R Getting Help Libraries and Packages Variables Vectors Arithmetic Data Frames Exporting Data Importing Data Internal Mathematical Functions Writing Your Own Functions Plotting Mathematical Functions Loops Making Decisions Scripts Reading Data from Websites Matrices and Linear Algebra Some Useful Functions and Operations CHAPTER 3 STATISTICS * Populations and Samples Mean Median Standard Deviation and Variance of a Sample Covariance and Correlation Visualizing Data Histograms Box Plots Plotting Data Sets Some Plotting Parameters and Commands Estimating Population Statistics Confidence Interval for the Population Mean Using Student's t Variables Confidence Interval for the Population Variance Using Chi-Square Variables Confidence Interval Interpretation Comparing the Means of Two Samples Testing Data for Normality Outlier Identification Modified Thompson Technique Chauvenet's Criterion * CHAPTER 4 CURVE FITS * Linear Regression Nonlinear Regression Kernel Smoothing CHAPTER 5 UNCERTAINTY OF A MEASURED QUANTITY * What Is Uncertainty? Random Variables Measurement Uncertainties Elemental Systematic Errors Normal Distributions Uniform Distributions Triangular Distributions CHAPTER 6 UNCERTAINTY OF A RESULT CALCULATED USING EXPERIMENTAL DATA * Taylor Series Approach. Coverage Factors The Kline-McClintock Equation Balance Checks CHAPTER 7 TAYLOR SERIES UNCERTAINTY OF A LINEAR REGRESSION CURVE FIT Curve-fit Expressions Cases to Consider: Case 1: No Errors and No Correlations Case 2: Random Errors Only Case 3: Random and Systematic Errors * General Linear Regression Theory Uncertainties in Regression Coefficients Evaluating Uncertainties with Built-in R functions * CHAPTER 8 MONTE CARLO METHODS * Overall Monte Carlo Approach Random Number Generation Accept/Reject Method Inverse-cdf Method *Random Sampling Uncertainty of a Measured Variable Bootstrapping with Internal Functions in R Monte Carlo Convergence Criteria Uncertainty of a Result Calculated Using Experimental Data Uncertainty Bands for Linear Regression Curve Fits Uncertainty Bands for a Curve Fit with Kernel Smoothing * CHAPTER 9 THE BAYESIAN APPROACH * Bayes Theorem for Probability Density Functions; Bayesian Estimation of the Mean and Standard Deviation of a Normal Population * APPENDIX PROBABILITY DENSITY FUNCTIONS * Univariate pdfs Normal Distribution Uniform Distribution Triangular Distribution Student's t Distribution Chi-Square Distribution Multivariate pdfs Marginal Distributions References *
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