Two features of "Processing Random Data" differentiate it from other similar books: the focus on computing the reproducibility error for statistical measurements, and its comprehensive coverage of Maximum Likelihood parameter estimation techniques. The book is useful for dealing with situations where there is a model relating to the input and output of a process, but with a random component, which could be noise in the system or the process itself could be random, like turbulence. Parameter estimation techniques are shown for many different types of statistical models, including joint Gaussian. The Cramer-Rao bounds are described as useful estimates of reproducibility errors. Finally, using an example with a random sampling of turbulent flows that can occur when using laser anemometry, the book also explains the use of conditional probabilities.
Author(s): Robert V. Edwards
Year: 2006
Language: English
Pages: 152
Contents ......Page 10
Dedication ......Page 6
Preface ......Page 8
1.1 Basic Concepts ......Page 14
1.3 Probability Distribution Functions ......Page 17
1.4 The Expected Value Process ......Page 24
1.5 Variance and Standard Deviation ......Page 25
1.6 Moments and Moment Generating Functions ......Page 27
1.7 Common Types of Distributions ......Page 28
1.8 Functions of More Than One Random Variable ......Page 41
1.9 Change of Variable ......Page 45
2.1 Variance of the Measured Mean ......Page 50
2.2 Estimate of the Variance ......Page 52
2.3 Variance of the Measured Variance ......Page 54
2.4 Non-independent Random Variables ......Page 58
2.5 Histograms ......Page 60
2.6 Confidence Limits ......Page 64
3.1 Averages ......Page 74
3.2 The Autocovariance and Autocorrelation Function ......Page 75
3.3 The Power Spectrum of a Random Signal ......Page 79
3.4 Processing Time Series by Computer ......Page 82
3.5 Estimation of the Autocorrelation ......Page 83
3.6 Estimation of the Power Spectrum of Time Series Data ......Page 89
3.7 Batch Mode Autocorrelation ......Page 95
4.1 Motivation ......Page 100
4.2 Maximum Likelihood Estimation ......Page 104
4.3 Residuals ......Page 111
4.4 Parameter Error Estimates ......Page 113
4.5 A Priori Error Estimation ......Page 119
4.6 Maximum A Posteriori Estimation ......Page 121
5.1 Basic Concepts of Random Sampling ......Page 128
5.2 Independent Sampling ......Page 129
5.3 Sample and Hold Autocorrelation and Spectrum Estimation ......Page 137
5.4 Non-independent Sampling ......Page 140
5.5 Photon Detection ......Page 147
Index ......Page 152
