Processing Random Data : Statistics For Engineers And Scientists - Robert V Edwards

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Processing Random Data

Statistics For Engineers And Scientists

By: Robert V Edwards

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Hardcover | 5 July 2006

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154 Pages

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22.86 x 15.24 x 1.12

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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.

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Preface	p. vii
Random Variables	p. 1
Basic Concepts	p. 1
Expected Values	p. 4
Probability Distribution Functions	p. 4
Properties of probability density functions	p. 10
The Expected Value Process	p. 11
Variance and Standard Deviation	p. 12
Moments and Moment Generating Functions	p. 14
Common Types of Distributions	p. 15
Uniform distribution	p. 15
Binomial distribution	p. 16
Using the binomial distribution	p. 19
Poisson distribution	p. 20
Gaussian (or normal) distribution	p. 23
Student-t distribution	p. 24
Sum of two Gaussian variables	p. 26
The Chi-squared distribution	p. 26
The error function	p. 27
Functions of More Than One Random Variable	p. 28
(Bayes theorem)	p. 28
Joint Gaussian distributions	p. 31
Change of Variable	p. 32
Measurement of Samples of Random Numbers	p. 37
Variance of the Measured Mean	p. 37
Estimate of the Variance	p. 39
Variance of the Measured Variance	p. 41
Non-Independent Random Variables	p. 45
Histograms	p. 47
Statistical experiments involving the uniform and binomial distributions	p. 48
Confidence Limits	p. 51
Tests of hypotheses	p. 53
Time Series-Random Variables that are Functions of Time	p. 61
Averages	p. 61
The Autocovariance and Autocorrelation Function	p. 62
Variance of the average of a signal with correlation	p. 63
The Power Spectrum of a Random Signal	p. 66
Short review of Fourier transforms	p. 67
Processing Time Series by Computer	p. 69
Estimation of the Autocorrelation	p. 70
Error covariance for autocorrelation estimates	p. 70
Random, correlated signal generator	p. 75
Estimation of the Power Spectrum of Time Series Data	p. 76
Generic properties of the digital Fourier transform	p. 77
The variance of spectrum estimates	p. 79
Batch Mode Autocorrelation	p. 82
Parameter Estimation	p. 87
Motivation	p. 87
Maximum Likelihood Estimation	p. 91
Gaussian processes	p. 92
Poisson processes	p. 94
Non-independent Gaussian statistics	p. 95
Chi-squared distributions	p. 97
Residuals	p. 98
Parameter Error Estimates	p. 100
Expected errors for Gaussian statistics	p. 103
Error estimates for joint Gaussian statistics	p. 105
Error estimates for Poisson processes	p. 106
Error estimates for Chi-square distributions	p. 106
A Priori Error Estimation	p. 106
Maximum A Posteriori Estimation	p. 108
Random Sampling	p. 115
Basic Concepts of Random Sampling	p. 115
Independent Sampling	p. 116
Mean and variance of the mean with random sampling	p. 117
Spectrum and autocorrelation estimate using randomly sampled data	p. 119
Effect of finite sample intervals [Delta]t	p. 124
Sample and Hold Autocorrelation and Spectrum Estimation	p. 124
Non-Independent Sampling	p. 127
Sample and hold (rate depends on f)	p. 129
Controlled sampling	p. 132
Autocorrelation estimation	p. 133
Photon Detection	p. 134
Moments	p. 134
Autocorrelation estimation	p. 135
Index	p. 139
Table of Contents provided by Ingram. All Rights Reserved.

Processing Random Data

Statistics For Engineers And Scientists

At a Glance

Hardcover

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