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Designing Quantitative Experiments : Prediction Analysis - John Wolberg

Designing Quantitative Experiments

Prediction Analysis

Paperback Published: 29th April 2010
ISBN: 9783642115882
Number Of Pages: 210

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Early in my career I was given the task of designing a sub-critical nuclear reactor facility that was to be used to perform basic research in the area of reactor physics. We planned to run a series of experiments to determine fundamental parameters related to the distribution of neutrons in such s- tems. I felt that it was extremely important to understand how the design would impact upon the accuracy of our results and as a result of this - quirement I developed a design methodology that I subsequently called prediction analysis. After working with this method for several years and applying it to a variety of different experiments, I wrote a book on the subject. Not surprisingly, it was entitled Prediction Analysis and was p- lished by Van Nostrand in 1967. Since the book was published over 40 years ago science and technology have undergone massive changes due to the computer revolution. Not - ly has available computing power increased by many orders of magnitude, easily available and easy to use software has become almost ubiquitous. In the 1960's my emphasis was on the development of equations, tables and graphs to help researchers design experiments based upon some we- known mathematical models. When I reconsider this work in the light of today's world, the emphasis should shift towards applying current techn- ogy to facilitate the design process.

Introductionp. 1
The Experimental Methodp. 1
Quantitative Experimentsp. 2
Dealing with Uncertaintyp. 3
Parametric Modelsp. 5
Basic Assumptionsp. 11
Treatment of Systematic Errorsp. 13
Nonparametric Modelsp. 16
Statistical Learningp. 18
Statistical Backgroundp. 19
Experimental Variablesp. 19
Measures of Locationp. 21
Measures of Variationp. 24
Statistical Distributionsp. 27
The normal distributionp. 28
The binomial distributionp. 30
The Poisson distributionp. 32
The x2 distributionp. 34
The t distributionp. 37
The F distributionp. 38
The Gamma distributionsp. 39
Functions of Several Variablesp. 40
The Method of Least Squaresp. 47
Introductionp. 47
The Objective Functionp. 50
Data Weightingp. 55
Obtaining the Least Squares Solutionp. 60
Uncertainty in the Model Parametersp. 66
Uncertainty in the Model Predictionsp. 69
Treatment of Prior Estimatesp. 75
Applying Least Squares to Classification Problemsp. 80
Goodness-of-Fitp. 81
The REGRESS Programp. 86
Prediction Analysisp. 90
Introductionp. 90
Linking Prediction Analysis and Least Squaresp. 91
Prediction Analysis of a Straight Line Experimentp. 92
Prediction Analysis of an Exponential Experimentp. 98
Dimensionless Groupsp. 103
Simulating Experimentsp. 106
Predicting Calculational Complexityp. 111
Predicting the Effects of Systematic Errorsp. 116
P.A. with Uncertainty in the Independent Variablesp. 118
Multiple Linear Regressionp. 120
Separation Experimentsp. 128
Introductionp. 128
Exponential Separation Experimentsp. 129
Gaussian Peak Separation Experimentsp. 136
Sine Wave Separation Experimentsp. 144
Bivariate Separationp. 150
Initial Value Experimentsp. 157
Introductionp. 157
A Nonlinear First Order Differential Equationp. 157
First Order ODE with an Analytical Solutionp. 162
Simultaneous First Order Differential Equationsp. 168
The Chemostatp. 172
Astronomical Observations using Kepler's Lawsp. 177
Random Distributionsp. 186
Introductionp. 186
Revisiting Multiple Linear Regressionp. 187
Bivariate Normal Distributionp. 191
Orthogonalityp. 196
Referencesp. 205
Indexp. 209
Table of Contents provided by Ingram. All Rights Reserved.

ISBN: 9783642115882
ISBN-10: 3642115888
Audience: General
Format: Paperback
Language: English
Number Of Pages: 210
Published: 29th April 2010
Publisher: Springer-Verlag Berlin and Heidelberg Gmbh & Co. Kg
Country of Publication: DE
Dimensions (cm): 22.86 x 15.24  x 1.52
Weight (kg): 0.32