فنی مهندسی

فرمت: pdf
حجم: 5.7 مگابایت
قیمت: 2000 تومان

Rational Descriptions, Decisions and Designs

By


شناسنامه فارسی کتاب:
عنوان کتاب:

توضیحات منطقی، تصمیم گیری و طراحی

موضوع کتاب:

Technique

سال نشر:
ناشر: Pergamon Press
ویرایش:
شماره جلد:
تعداد صفحه: 489
زبان: انگلیسی
Rational Descriptions, Decisions and Designs is a reference for understanding the aspects of rational decision theory in terms of the basic formalism of information theory. The text provides ways to achieve correct engineering design decisions.
The book starts with an understanding for the need to apply rationality, as opposed to uncertainty, in design decision making. Inductive logic in computers is explained where the design of the machine and the accompanying software are considered. The text then explains the functional equations and the problems of arriving at a rational description through some mathematical preliminaries. Bayes' equation and rational inference as tools for adjusting probabilities when something new is encountered in earlier probability distributions are explained. The book presents as well a case study concerning the error made in following specifications of spark plugs. The author also explains the Bernoulli trials, where a probability that a better hypothesis than that already adopted may exist. The rational measure of uncertainty and the principle of maximum entropy with sample calculations are included in the text. After considering the probabilities, the decision theory is taken up where engineering design follows. Examples regarding transmitter and voltmeter designs are presented. The book ends by explaining probabilities of success and failure as applied to reliability engineering, that it is a state of knowledge rather than the state of a thing.
The text can serve as a textbook for students in technology engineering and design, and as a useful reference for mathematicians, statisticians, and fabrication engineers.
Foreword xi

Preface xv

Concerning the Use of the Book as a Text xix


1. What Do We Mean by Rational? 1

What Has the Concern for Rationality to Do With Design? 2
Inductive Logic 3
Desiderata for an Inductive Logic Computer 4
A First Consequence of the Desiderata 6
A Second Consequence of the Desiderata 13
The Functional Equations 14
A Solution to the Functional Equation 18
A Second Functional Relation 21
A Particular Choice of Variable 24
Concerning Allowable Transformations 26
The Problem of Inference 29
Appendix A-The Solution to the First Functional Equation 31
Appendix B-The Solution to the Second Functional Equation 34


2. Rational Descriptions, Some Mathematical Preliminaries 37

Probability of an "OR" Statement 37
A Geometrical Interpretation of the Additive Rules 38
Contingency Table 39
The Encoding of Symmetrical Knowledge 48
Unsymmetrical Consequences of Symmetrical Knowledge 50
The Concept of a Bernoulli Trial 51
The Multinomial Distribution 53
Stirling's Approximation for n! and log n! 54
The Probability of a Particular Frequency 54 The Concept of Expectation 60
Expectations and Mathematical Expectations 62
The Variance and Higher Moments 63
Additional Remarks on the Difference Between Frequency and Probability 65
Continuous Distributions 67
Deterministic Knowledge About a Discrete or Continuous Variable 71


3. Bayes' Equation and Rational Inference 73

Bayes' Equation 74
Bayes' Equation and the Role of Prior Probabilities-The Extension Rule 78
On the Futility of Arguments over the Need for Prior Probabilities 80
The Concept of Statistical Dependence 82
Hypothesis Testing and the Evidence Form of Bayes' Equation 83
Example Problem: The Spark Plug Manufacturer 86
Multiple Outcomes and Non-Bernoulli Processes 93
Is There a Hypothesis We Had Not Considered? 96
The Chi-Square Test of an Hypothesis 101
Test of a Random Number Generator 104


4. A Rational Measure of Uncertainty 107

Entropy as a Measure of Uncertainty 111
The Use of Other than Binary Questions 114


5. The Principle of Maximum Entropy 119

The Maximum Entropy Formalism 120
Proof that S is at a Maximum and not a Local Saddle Point 123
Some Properties of the Maximum Entropy Distribution 124
Maximum Entropy Probability Distributions 127
The Uniform Distribution 128
The Exponential Distribution 129
The Truncated and the Normal Gaussian Distributions 131
The Gamma Distribution 144
The Incomplete Gamma Function 148
The Beta Distribution 150
Some Other Probability Distributions 154
Entropy and Hypothesis Testing 156
Some Sample Calculations 159
Appendix C-The Error Function and its Approximation 167
Appendix D-Using the Digamma F...
شابک/ISBN: 978-1483113814