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雷达卡
By: Jack R Benjamin, C. Allin Cornell
Designed as a primary text for civil engineering courses, as a supplementary text for courses in other areas, or for self-study by practicing engineers, this text covers the development of decision theory and the applications of probability within the field. Extensive use of examples and illustrations helps readers develop an in-depth appreciation for the theory's applications, which include strength of materials, soil mechanics, construction planning, and water-resource design.
A focus on fundamentals includes such subjects as Bayesian statistical decision theory, subjective probability, and utility theory. This makes the material accessible to engineers trained in classical statistics and also provides a brief elementary introduction to probability. The coverage also addresses in detail the methods for analyzing engineering economic decisions in the face of uncertainty. An Appendix of tables makes this volume particularly useful as a reference text.
Contents
Preface
Introduction
Chapter 1 Data Reduction
1.1 Graphical Displays
1.2 Numerical Summaries
1.3 Data Observed in Pairs
1.4 Summary for Chapter 1
Chapter 2 Elements of Probability Theory
2.1 Random Events
2.1.1 Sample Space and Events
2.1.2 Probability Measure
2.1.3 Simple Probabilities of Events
2.1.4 Summary
2.2 Random Variables and Distributions
2.2.1 Random Variables
2.2.2 Jointly Distributed Random Variables
2.3 Derived Distributions
2.3.1 One-variable Transformations: Y = g(X)
2.3.2 Functions of Two Random Variables
2.3.3 Elementary Simulation
2.3.4 Summary
2.4 Moments and Expectation
2.4.1 Moments of a Random Variable
2.4.2 Expectation of a Function of a Random Variable
2.4.3 Expectation and Jointly Distributed Random Variables
2.4.4 Approximate Moments and Distributions of Functions
2.4.5 Summary
2.5 Summary for Chapter 2
Chapter 3 Common Probabilistic Models
3.1 Models from Simple Discrete Random Trials
3.1.1 A Single Trial: The Bernoulli Distribution
3.1.2 Repeated Trials: The Binomial Distribution
3.1.3 Repeated Trials: The Geometric and Negative Binomial Distributions
3.1.4 Summary
3.2 Models from Random Occurrences
3.2.1 Counting Events: The Poisson Distribution
3.2.2 Time between Events: The Exponential Distribution
3.2.3 Time to the kth Event: The Gamma Distribution
3.2.4 Summary
3.3 Models from Limiting Cases
3.3.1 The Model of Sums: The Normal Distribution
3.3.2 The Model of Products: The Lognormal Distribution
3.3.3 The Model of Extremes: The Extreme Value Distributions
3.3.4 Summary
3.4 Additional Common Distributions
3.4.1 The Equally Likely Model: The Rectangular or Uniform Distribution
3.4.2 The Beta Distribution
3.4.3 Some Normal Related Distributions: Chi-square, Chi, t, and F
3.4.4 Summary
3.5 Modified Distributions
3.5.1 Shifted and Transformed Distributions
3.5.2 Truncated and Censored Distributions
3.5.3 Compound Distributions
3.5.4 Summary
3.6 Multivariate Models
3.6.1 Counting Multiple Events: The Multinomial Distribution
3.6.2 The Multivariate Normal Distribution
3.6.3 Summary
3.7 Markov Chains
3.7.1 Simple Markov Chains
3.7.2 Two-state Homogeneous Chains
3.7.3 Multistate Markov Chains
3.7.4 Summary
3.8 Summary for Chapter 3
Chapter 4 Probabilistic Models and Observed Data
4.1 Estimation of Model Parameters
4.1.1 The Method of Moments
4.1.2 The Properties of Estimators: Their First- and Second-order Moments
4.1.3 The Distributions of Estimators and Confidence-interval Estimation
4.1.4 The Method of Maximum Likelihood
4.1.5 Summary
4.2 Significance Testing
4.2.1 Hypothesis Testing
4.2.2 Some Common Hypothesis Tests
4.2.3 Summary
4.3 Statistical Analysis of Linear Models
4.3.1 Linear Models
4.3.2 Statistical Analysis of Simple Linear Models
4.3.3 Summary
4.4 Model Verification
4.4.1 Comparing Shapes: Histograms and Probability Paper
4.4.2 “Goodness-of-fit” Significance Tests
4.4.3 Summary
4.5 Empirical Selection of Models
4.5.1 Model Selection: Illustration I, Loading Times
4.5.2 Model Selection: Illustration II, Maximum Annual Flows
4.5.3 Summary
4.6 Summary of Chapter 4
Chapter 5 Elementary Bayesian Decision Theory
5.1 Decisions with Given Information
5.1.1 The Decision Model
5.1.2 Expected-value Decisions
5.1.3 Probability Assignments
5.1.4 Analysis of the Decision Tree with Given Information
5.1.5 Summary
5.2 Terminal Analysis
5.2.1 Decision Analysis Given New Information
5.2.2 Summary
5.3 Preposterior Analysis
5.3.1 The Complete Decision Model
5.3.2 Summary
5.4 Summary for Chapter 5
Chapter 6 Decision Analysis of Independent Random Processes
6.1 The Model and Its Prior Analysis
6.1.1 Prior Analysis of the Special Problem u(a, X)
6.1.2 More General Relationships between the Process and the State of Interest
6.1.3 Summary
6.2 Terminal Analysis Given Observations of the Process
6.2.1 The General Case
6.2.2 Data-based Decisions: Diffuse Priors
6.2.3 Use of Conjugate Priors
6.2.4 Summary
6.3 The Bayesian Distribution of a Random Variable
6.3.1 The Simple Case; X Only
6.3.2 The General Case Y = h(X1 X2, . . ., Xβ)
6.3.3 Summary
6.4 Summary of Chapter
Appendix A Tables
Table A.1 Values of the Standardized Normal Distribution
Table A.2 Tables for Evaluation of the CDF of the χ2, Gamma, and Poisson Distributions
Table A.3 Cumulative Distribution of Student’s t Distribution
Table A.4 Properties of Some Standardized Beta Distributions
Table A.5 Values of the Standardized Type I Extreme-value Distribution
Table A.6 F Distribution; Value of z such that Fz(z) = 0.95
Table A.7 Critical Statistic for the Kolmogorov-Smirnov Goodness-of-fit Test
Table A.8 Table of Random Digits
Appendix B Derivation of the Asymptotic Extreme-value Distribution
Name Index
Subject Index
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