Cover......Page 1
Statistics and Probability Theory......Page 4
Preface......Page 7
Acknowledgements......Page 10
Contents......Page 11
1.1 Introduction......Page 15
1.2 Societal Decision Making and Risk......Page 16
1.2.1 Example 1.1-Feasibility of Hydraulic Power Plant......Page 17
1.3 Definition of Risk......Page 20
1.4 Self Assessment Questions/Exercises......Page 21
2.1 Introduction......Page 22
2.2.1 Frequentistic Definition......Page 23
2.2.3 Bayesian Definition......Page 24
2.3 Sample Space and Events......Page 25
2.5 Conditional Probability and Bayes' Rule......Page 27
2.5.1 Example 2.1-Using Bayes' Rule for Concrete Assessment......Page 29
2.5.2 Example 2.2-Using Bayes' Rule for Bridge Upgrading......Page 30
2.6 Self Assessment Questions/Exercises......Page 31
3.1 Introduction......Page 34
3.2.2 Example 3.1-Concrete Compressive Strength Data......Page 35
3.2.3 Example 3.2-Traffic Flow Data......Page 36
3.2.4 Dispersion Measures......Page 37
3.2.5 Other Measures......Page 38
3.2.7 Measures of Correlation......Page 39
3.3 Graphical Representations......Page 40
3.3.2 Histograms......Page 41
3.3.3 Quantile Plots......Page 44
3.3.4 Tukey Box Plots......Page 49
3.3.5 Q-Q Plots and Tukey Mean-Difference Plot......Page 52
3.4 Self Assessment Questions/Exercises......Page 54
4.1 Introduction......Page 56
4.2 Uncertainties in Engineering Problems......Page 57
4.3 Random Variables......Page 59
4.3.1 Cumulative Distribution and Probability Density Functions......Page 60
4.3.2 Moments of Random Variables and the Expectation Operator......Page 61
4.3.3 Example 4.1-Uniform Distribution......Page 62
Lecture 5 (Aim of the Present Lecture)......Page 63
4.3.4 Properties of the Expectation Operator......Page 64
4.3.5 Random Vectors and Joint Moments......Page 65
4.3.6 Example 4.2-Linear Combinations and Random Variables......Page 66
4.3.7 Conditional Distributions and Conditional Moments......Page 67
4.3.8 The Probability Distribution for the Sum of Two Random Variables......Page 68
4.3.9 Example 4.3-Density Function for the Sum of Two Random Variables-Special Case Normal Distribution......Page 70
4.3.10 The Probability Distribution for Functions of Random Variables......Page 71
4.3.11 Example 4.4-Probability Distribution for a Function of Random Variables......Page 72
4.3.12 Probability Density and Distribution Functions......Page 74
4.3.13 The Central Limit Theorem and Derived Distributions......Page 75
4.3.15 The Normal Distribution......Page 77
4.4 Stochastic Processes and Extremes......Page 80
4.4.1 Random Sequences-Bernoulli Trials......Page 81
Lecture 7 (Aim of the Present Lecture)......Page 82
4.4.3 The Poisson Counting Process......Page 83
4.4.4 Continuous Random Processes......Page 84
4.4.5 Stationarity and Ergodicity......Page 87
4.4.6 Statistical Assessment of Extreme Values......Page 88
4.4.7 Extreme Value Distributions......Page 89
4.4.8 Type I Extreme Maximum Value Distribution-Gumbel Max......Page 90
4.4.10 Type II Extreme Maximum Value Distribution-Fréchet Max......Page 92
4.4.11 Type III Extreme Minimum Value Distribution-Weibull Min......Page 93
4.4.13 Example 4.7-A Flood with a 100-Year Return Period......Page 94
4.5 Self Assessment Questions/Exercises......Page 95
Lecture 8 (Aim of the Present Lecture)......Page 98
5.1 Introduction......Page 99
5.2 Selection of Probability Distributions......Page 100
5.2.1 Model Selection by Use of Probability Paper......Page 101
5.3.1 The Method of Moments......Page 104
5.3.2 The Method of Maximum Likelihood......Page 105
5.3.3 Example 5.1-Parameter Estimation......Page 106
Lecture 9 (Aim of the Present Lecture)......Page 108
5.4 Bayesian Estimation Methods......Page 109
5.4.1 Example 5.2-Yield Stress of a Steel Bar......Page 110
5.5 Bayesian Regression Analysis......Page 112
5.5.1 Linear Regression: Prior Model......Page 113
5.5.2 Example 5.3-Tensile Strength of Timber: Prior Model......Page 115
5.5.4 Example 5.4-Updating Regression Coefficients (Determined in Example 5.3)......Page 117
5.6 Probability Distributions in Statistics......Page 119
5.6.1 The Chi-Square (chi2)-Distribution......Page 120
5.7 Estimators for Sample Descriptors-Sample Statistics......Page 121
5.7.1 Statistical Characteristics of the Sample Average......Page 122
5.7.2 Statistical Characteristics of the Sample Variance......Page 124
5.7.3 Confidence Intervals......Page 125
5.8 Testing for Statistical Significance......Page 126
5.8.1 The Hypothesis Testing Procedure......Page 127
5.8.3 Some Remarks on Testing......Page 129
5.9 Model Evaluation by Statistical Testing......Page 130
5.9.1 The Chi-Square (chi2)-Goodness of Fit Test......Page 131
5.9.2 The Kolmogorov-Smirnov Goodness of Fit Test......Page 135
5.9.3 Model Comparison......Page 137
5.10 Self Assessment Questions/Exercises......Page 138
6.1 Introduction......Page 141
6.2 Failure Events and Basic Random Variables......Page 142
6.3 Linear Limit State Functions and Normal Distributed Variables......Page 143
6.3.1 Example 6.1-Reliability of a Steel Rod-Linear Safety Margin......Page 144
6.4 The Error Propagation Law......Page 145
6.4.1 Example 6.2-Error Propagation Law......Page 147
6.5 Non-linear Limit State Functions......Page 148
6.5.1 Example 6.3-FORM-Non-linear Limit State Function......Page 149
6.6 Simulation Methods......Page 151
6.6.1 Example 6.4: Monte Carlo Simulation......Page 152
6.7 Self Assessment Questions/Exercises......Page 154
Lecture 13 (Aim of the Present Lecture)......Page 155
7.2 The Decision/Event Tree......Page 156
7.3 Decisions Based on Expected Values......Page 157
7.5 Decision Analysis with Given Information-Prior Analysis......Page 159
7.6 Decision Analysis with Additional Information-Posterior Analysis......Page 160
7.7 Decision Analysis with `Unknown' Information-Pre-posterior Analysis......Page 163
7.8 The Risk Treatment Decision Problem......Page 164
7.9 Self Assessment Questions/Exercises......Page 166
A.1 Chapter 1......Page 167
A.2 Chapter 2......Page 168
A.3 Chapter 3......Page 170
A.4 Chapter 4......Page 171
A.5 Chapter 5......Page 173
A.6 Chapter 6......Page 175
A.7 Chapter 7......Page 179
B.1.2 Equation 5.71......Page 182
B.1.3 Examples on Chi-Square Significance Test......Page 183
B.2.2 Example 6.3......Page 184
Appendix C: Tables......Page 187
References......Page 194
Index......Page 195
