Designing Quantitative Experiments

Prediction Analysis

By: John Wolberg

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Paperback | 6 May 2010

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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.

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Introduction	p. 1
The Experimental Method	p. 1
Quantitative Experiments	p. 2
Dealing with Uncertainty	p. 3
Parametric Models	p. 5
Basic Assumptions	p. 11
Treatment of Systematic Errors	p. 13
Nonparametric Models	p. 16
Statistical Learning	p. 18
Statistical Background	p. 19
Experimental Variables	p. 19
Measures of Location	p. 21
Measures of Variation	p. 24
Statistical Distributions	p. 27
The normal distribution	p. 28
The binomial distribution	p. 30
The Poisson distribution	p. 32
The x² distribution	p. 34
The t distribution	p. 37
The F distribution	p. 38
The Gamma distributions	p. 39
Functions of Several Variables	p. 40
The Method of Least Squares	p. 47
Introduction	p. 47
The Objective Function	p. 50
Data Weighting	p. 55
Obtaining the Least Squares Solution	p. 60
Uncertainty in the Model Parameters	p. 66
Uncertainty in the Model Predictions	p. 69
Treatment of Prior Estimates	p. 75
Applying Least Squares to Classification Problems	p. 80
Goodness-of-Fit	p. 81
The REGRESS Program	p. 86
Prediction Analysis	p. 90
Introduction	p. 90
Linking Prediction Analysis and Least Squares	p. 91
Prediction Analysis of a Straight Line Experiment	p. 92
Prediction Analysis of an Exponential Experiment	p. 98
Dimensionless Groups	p. 103
Simulating Experiments	p. 106
Predicting Calculational Complexity	p. 111
Predicting the Effects of Systematic Errors	p. 116
P.A. with Uncertainty in the Independent Variables	p. 118
Multiple Linear Regression	p. 120
Separation Experiments	p. 128
Introduction	p. 128
Exponential Separation Experiments	p. 129
Gaussian Peak Separation Experiments	p. 136
Sine Wave Separation Experiments	p. 144
Bivariate Separation	p. 150
Initial Value Experiments	p. 157
Introduction	p. 157
A Nonlinear First Order Differential Equation	p. 157
First Order ODE with an Analytical Solution	p. 162
Simultaneous First Order Differential Equations	p. 168
The Chemostat	p. 172
Astronomical Observations using Kepler's Laws	p. 177
Random Distributions	p. 186
Introduction	p. 186
Revisiting Multiple Linear Regression	p. 187
Bivariate Normal Distribution	p. 191
Orthogonality	p. 196
References	p. 205
Index	p. 209
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Prediction Analysis

At a Glance

Paperback

Shipping

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