Articoli correlati a Statistics and Probability Theory: In Pursuit of Engineering...
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ENGINEERING DECISIONS UNDER UNCERTAINTY.- Lecture 1.- 1.1 Introduction.- 1.2 Societal Decision Making and Risk.- 1.2.1 Example 1.1 - Feasibility of Hydraulic Power Plant .- 1.3 Definition of Risk.- 1.4 Self Assessment Questions / Exercises .- 2 BASIC PROBABILITY THEORY .- Lecture 2.- 2.1 Introduction .- 2.2 Definition of Probability.- 2.2.1 Frequentistic Definition.- 2.2.3 Bayesian Definition.- 2.2.4 Practical Implications of the Different Interpretations of Probability.- 2.3 Sample Space and Events.- 2.4 The three Axioms of Probability Theory.- 2.5 Conditional Probability and Bayes' Rule.- 2.5.1 Example 2.1 - Using Bayes' Rule for Concrete Assessment .- 2.5.2 Example 2.2 - Using Bayes' Rule for Bridge Upgrading.- 2.6 Self Assessment Questions / Exercises.- 3 DESCRIPTIVE STATISTICS.- Lecture 3 .- 3.1 Introduction.- 3.2 Numerical Summaries.- 3.2.1 Central Measures.- 3.2.2 Example 3.1 - Concrete Compressive Strength Data.- 3.2.3 Example 3.2 - Traffic Flow Data.- 3.2.4 Dispersion Measures.- 3.2.5 Other Measures.- 3.2.6 Sample Moments and Sample Central Moments.- 3.2.7 Measures of Correlation.- 3.3 Graphical Representations.- 3.3.1 One-Dimensional Scatter Diagrams.- 3.3.2 Histograms.- 3.3.3 Quantile Plots.- 3.3.4 Tukey Box Plots.- 3.3.5 Q-Q Plots and Tukey Mean-Difference Plot.- 3.4 Self Assessment Questions / Exercises.- 4 UNCERTAINTY MODELLING.- Lecture 4.- 4.1 Introduction.- 4.2 Uncertainties in Engineering Problems.- 4.3 Random Variables.- 4.3.1 Cumulative Distribution and Probability Density Functions.- 4.3.2 Moments of Random Variables and the Expectation Operator.- 4.3.3 Example 4.1 - Uniform distribution.- Lecture 5.- 4.3.4 Properties of the Expectation Operator.- 4.3.5 Random Vectors and Joint Moments.- 4.3.6 Example 4.2 - linear combinations and random variables.- 4.3.7 Conditional Distributions and Conditional Moments .- 4.3.8 The Probability Distribution for the Sum of two Random Variables .- 4.3.9 Example 4.3 - Density Function for the Sum of two Random Variables - Special Case Normal Distribution.- 4.3.10 The Probability Distribution for Functions of Random Variables .- 4.3.11 Example 4.4 - Probability Distribution for a Function of Random Variables.- Lecture 6.- 4.3.12 Probability Density and Distribution Functions.- 4.3.13 The Central Limit Theorem and Derived Distributions.- 4.3.14 Example 4.5 - Central Limit Theorem.- 4.3.15 The Normal Distribution.- 4.3.16 The Lognormal Distribution.- 4.4 Stochastic Processes and Extremes.- 4.4.1 Random Sequences - Bernoulli Trials.- 4.4.2 Example 4.6 - Quality Control of Concrete.- Lecture 7 .- 4.4.3 The Poisson Counting Process .- 4.4.4 Continuous Random Processes.- 4.4.5 Stationarity and Ergodicity.- 4.4.6 Statistical Assessment of Extreme Values.- 4.4.7 Extreme Value Distributions.- 4.4.8 Type I Extreme Maximum Value Distribution - Gumbel max.- 4.4.9 Type I Extreme Minimum Value Distribution - Gumbel min.- 4.4.10 Type II Extreme Maximum Value Distribution - Frechet max.- 4.4.11 Type III Extreme Minimum Value Distribution - Weibull min.- 4.4.12 Return Period for Extreme Events.- 4.4.13 Example 4.7 - A Flood with a 100-Year Return Period.- 4.5 Self Assessment Questions / Exercises.- 5 ESTIMATION AND MODEL BUILDING.- Lecture 8.- 5.1 Introduction .- 5.2 Selection of Probability Distributions.- 5.2.1 Model Selection by Use of Probability Paper.- 5.3 Estimation of Distribution Parameters.- 5.3.1 The Method of Moments.- 5.3.2 The Method of Maximum Likelihood.- 5.3.3 Example 5.1 - Parameter Estimation.- Lecture 9.- 5.4 Bayesian Estimation Methods.- 5.4.1 Example 5.2 - Yield Stress of a Steel Bar.- 5.5 Bayesian Regression Analysis.- 5.5.1 Linear Regression: Prior Model.- 5.5.2 Example 5.3 - Tensile Strength of Timber: Prior Model.- 5.5.3 Updating Regression Coefficients: Posterior Model.- 5.5.4 Example 5.4 - Updating Regression Coefficients (determined in Example 5.3).- Lecture 10.- 5
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