Uncertainty Quantification and Stochastic Modelling with EXCEL (Springer Texts in Business and Economics)

✍ Scribed by Eduardo Souza de Cursi

• Publisher: Springer
• Year: 2022
• Tongue: English
• Leaves: 536
• Category: Library

✦ Synopsis

This book presents techniques for determining uncertainties in numerical solutions with applications in the fields of business administration, civil engineering, and economics, using Excel as a computational tool. Also included are solutions to uncertainty problems involving stochastic methods. The list of topics specially covered in this volume includes linear and nonlinear programming, Lagrange multipliers (for sensitivity), multi objective optimization, and Game Theory, as well as linear algebraic equations, and probability and statistics. The book also provides a selection of numerical methods developed for Excel, in order to enhance readers’ understanding. As such, it offers a valuable guide for all graduate and undergraduate students in the fields of economics, business administration, civil engineering, and others that rely on Excel as a research tool.

✦ Table of Contents

Introduction
Contents
1: Some Tips to Use EXCEL
1.1 How to Activate the SOLVER and the ANALYSIS TOOLPACK
1.2 How to Include a Third-Part Add-In
1.3 Disabling Warnings on the Add-Ins
1.4 How to Activate the VBA Tools
1.5 How to Insert a VBA Module
1.6 How to Import a VBA Module
1.7 Matrix Formulas
1.8 Fixing Volatile Formulas
1.9 Using Addresses of Cells
1.10 Using Names in EXCEL
1.11 How to Run the SOLVER
1.12 How to Include Iterative Calculations in Your Workbook
1.13 How to Include a Control in Your Workbook
1.14 How to Include a Chart in Your Workbook
1.15 How to Use a Variant to Store Anything in a Variable
1.16 How to Use a Collection to Store Anything in a Variable
1.17 How to Include a Class in Your Workbook
1.17 Remark
2: Some Useful Numerical Methods
2.1 Linear Systems
2.1.1 Using the Inverse Matrix
2.1.2 Using the SOLVER
2.1.3 Using Gauss-Jordan Pivoting
2.1.4 Using LU Decomposition
2.1.5 Using QR Decomposition
2.1.6 Using Relaxation Iterations
2.2 Optimization
2.2.1 Unconstrained Optimization Using the SOLVER in a Worksheet
2.2.2 Unconstrained Optimization Using the SOLVER in VBA
2.2.3 Constrained Optimization Using the SOLVER in a Worksheet
2.2.4 Constrained Optimization Using the SOLVER in VBA
2.2.5 Linear Programming Using the SOLVER in a Worksheet
2.2.6 Linear Programming Using the SOLVER in VBA
2.3 Nonlinear Equations
2.3.1 Nonlinear Equations Using the SOLVER in a Worksheet
2.3.2 Nonlinear Equations Using the SOLVER in VBA
2.3.3 Nonlinear Equations Using Newton-Raphson
2.3.4 Overdetermined Linear Systems
2.4 Ordinary Differential Equations
2.4.1 Runge-Kutta´s Methods
2.5 Numerical Integration
2.6 Multiobjective Optimization
2.7 Interpolation of Discrete Numerical Data
2.8 Numerical Derivatives
3: Probabilities with EXCEL
3.1 Probability
3.1 Example
3.1.1 Mass Functions and Mass Densities
3.1 Example
3.1 Example
3.1 Exercises
3.1.2 The Case of Finite Populations
3.1 Exercises
3.2 Combinatorial Probabilities with EXCEL
3.2 Example
3.2 Example
3.2 Exercises
3.3 Conditional Probability, Bayes´ Formula, and Independence
3.3 Example
3.3 Example
3.3 Exercises
3.4 Random Variables
3.4 Remark
3.4 Exercises
3.4.1 Statistics of a Random Variable
3.4 Remark
3.4 Example
3.4 Example
3.4 Exercises
3.4.2 Numerical Evaluation of Statistics
3.4 Example
3.4 Exercises
3.4.3 Classical Inequalities
3.4 Exercises
3.4.4 Characteristic Function and Moments
3.4 Exercises
3.5 Random Vectors and Pairs of Random Variables
3.5 Remark
3.5 Example
3.5 Example
3.5 Example
3.5 Example
3.5 Exercises
3.6 Discrete and Continuous Random Variables
3.6.1 Discrete Variables
3.6.2 Continuous Variables Having a PDF
3.6 Exercises
3.6 Supplementary Exercises
3.7 Sequences of Random Variables
3.7 Theorem (Lévy):
3.7 Example
3.7 Theorem:
3.7 Exercises
3.8 Samples
3.8 Theorem (Central Limit):
3.8 Theorem (Cochran):
3.8 Example
3.8 Remark
3.8 Example
3.8 Example
3.8 Exercises
3.8.1 Maximum Likelihood Estimators
3.8 Example
3.8 Exercises
3.8.2 Samples from Random Vectors
3.8 Example
3.8.3 Empirical CDF and Empirical PDF
3.8 Example
3.8 Example
3.9 Frequentist Probabilities with EXCEL
3.9.1 Testing Adequacy to a Distribution
3.9 Theorem (Fisher-Pearson):
3.9 Example
3.9 Example
3.9 Example
3.9 Exercises
3.9.2 Testing Independence
3.9 Example
3.9 Example
3.9 Exercises
3.10 Generating Uniform Random numbers
3.10.1 Using Built-In Functions
3.10.2 Using the Data Analysis Tool
3.10.3 Using VBA
3.11 Generating Normal Random Numbers
3.11.1 Using Built-In Functions
3.11.2 Using the Analysis ToolPack
3.11.3 Using VBA
3.12 Generating Triangular Random Numbers
3.13 Generating Random Numbers by Inversion
3.14 Generating Discrete Random Numbers
3.14.1 Using Built-In Functions
3.14.2 Using the Analysis Toolpack
3.14.3 Using VBA
3.15 Generating Regular Random Functions
3.15 Example
3.15 Example
3.16 Generating Regular Random Curves
3.16 Example
3.16 Example
4: Stochastic Processes
4.1 Stationarity and Ergodicity
4.1 Example
4.1 Example
4.1 Example
4.1 Example
4.1 Example
4.1 Exercises
4.2 Determination of the Distribution of a Stationary Process
4.2 Example
4.3 White Noise
4.3 Remark
4.4 Moving Average Processes
4.4 Theorem (Wold)
4.4 Example
4.4 Remark
4.4 Exercises
4.5 Autoregressive Processes
4.5 Theorem
4.5 Remark
4.5 Example
4.5 Exercises
4.6 ARMA Processes
4.6 Example
4.6 Exercises
4.7 Markov Processes
4.7 Example
4.7 Example
4.7 Example
4.7 Exercises
4.8 Diffusion Processes
4.8.1 Time Integral and Derivative of a Process
4.8 Example
4.8 Example
4.8 Exercises
4.8.2 Simulation of the Time Integral of a White Noise
4.8 Example
4.8 Example
4.8 Exercises
4.8.3 Brownian Motion
4.8 Example
4.8 Example
4.8 Exercises
4.8.4 Random Walks
4.8 Example
4.8 Example
4.8 Remark
4.8 Exercises
4.8.5 Itô´s Integrals
4.8 Remark
4.8.6 Itô´s Calculus
4.8 Example
4.8 Example
4.8 Example
4.8 Example
4.8.7 Numerical Simulation of Stochastic Differential Equations
4.8 Example
4.8 Example
4.8 Example
4.8 Example
4.8 Example
4.8 Exercises
5: Representation of Random Variables
5.1 The UQ Approach for the Representation of Random Variables
5.1 Problem
5.2 Collocation
5.2.1 Finding the Coefficients of the Expansion in a Worksheet
5.2.2 Solution Using VBA
5.2.3 Solution Using an Adapted Workbook
5.2 Exercises
5.3 Variational Approximation
5.3.1 Finding the Coefficients of the Expansion in a Worksheet
5.3.2 Solution Using VBA
5.3.3 Solution Using an Adapted Workbook
5.3 Exercises
5.4 Moments Matching Method
5.4.1 The Standard Formulation of M3
5.4.2 Constrained Optimization Formulation of M3
5.4.3 Multiobjective Optimization Formulation of M3
5.4 Exercises
5.5 Multidimensional Expansions
5.5.1 Case Where U Is Multidimensional
5.5 Example
5.5.2 Case Where X Is Multidimensional
5.5 Example
5.5 Exercises
5.6 Random Functions
5.6 Example
5.6 Example
5.6 Example
5.6 Exercises
5.7 Random Curves
5.7 Example
5.7 Example
5.7 Exercises
5.8 Mean, Variance and Confidence Intervals for Random Functions or Random Curves
5.8 Example
5.8 Example
5.8 Example
5.8 Example
5.8 Example
5.8 Example
5.8 Example
5.8 Example
5.8 Exercises
6: Uncertain Algebraic Equations
6.0 Exercises
6.1 Uncertain Linear Systems
6.1 Example
6.1 Example
6.1.1 Very Small Linear Systems
6.1 Example
6.1 Example
6.1 Exercises
6.2 Nonlinear Equations and Adaptation of an Iterative Code
6.2 Exercises
6.3 Iterative Evaluation of Eigenvalues
6.3.1 Very Small Matrices
6.3 Exercises
7: Random Differential Equations
7.1 Linear Differential Equations
7.1 Exercises
7.2 Nonlinear Differential Equations
7.2 Exercises
7.3 Uncertainties on Curves Connected to Differential Equations
7.3 Example
7.3 Example
7.3 Exercises
8: UQ in Game Theory
8.1 Language from Game Theory
8.2 A Simple Coin Game
8.2.1 GT Strategies When p Is Known
8.2.2 UQ Strategies When p Is Known
8.2.3 Strategies When p Is Unknown
8.2.4 Strategies for the Stochastic Game
8.2.5 Replicator Dynamics
8.3 A Classical Game: Prisoner´s Dilemma
8.3.1 Replicator Dynamics
8.4 The Goalie´s Anxiety at the Penalty Kick
8.4 Exercises
9: Optimization Under Uncertainty
9.1 Using the Methods of Representation
9.1 Example
9.1 Example
9.1 Exercises
9.2 Using the Adaptation of a Descent Method
9.2 Exercises
9.3 Combining Statistics of the Objective, the Constraints and Expansions
9.3 Exercises
10: Reliability
10.1 Reliability
10.1 Example
10.1 Example
10.1 Example
10.1 Exercises
10.2 Limit State Curves
10.2 Example
10.2 Example
10.2 Exercises
10.3 Design Point
10.3 Example
10.3.1 Multiple Failure Conditions
10.3 Example
10.3 Example
10.3 Exercises
10.4 Reliability Analysis
10.4 Example
10.4 Example
10.4 Exercises
10.5 Hasofer-Lind Reliability Index
10.5.1 The General Case
10.5 Example
10.5 Example
10.5 Example
10.5 Exercises
10.5.2 The Case of Affine Limit State Equations
10.5 Example
10.5 Example
10.5 Exercises
10.5.3 The Case of a Convex Failure Region
10.5 Example
10.5 Example
10.5 Exercises
10.6 Using the Reliability Index to Estimate the Probability of Failure
10.6 Example
10.6 Exercises
10.6.1 The Case of Affine Limit State Equations
10.6 Example
10.6 Exercises
10.6.2 The Case of a Convex Failure Region
10.6 Example
10.6 Exercises
10.6.3 General Failure Regions
10.6 Example
10.6 Example
10.6 Example
10.6 Exercises
10.7 The Transformations of Rosenblatt and Nataf
10.7 Example
10.7 Example
10.7 Exercises
10.8 FORM and SORM
10.8.1 First Order Reliability Method (FORM)
10.8 Example
10.8 Example
10.8 Exercises
10.8.2 Second Order Reliability Method (SORM)
10.8 Example
10.8 Example
10.8 Exercises
10.9 Reliability Based Design Optimization
10.9.1 The Bilevel or Double Loop Approach for a Desired β
10.9 Example
10.9 Example
10.9 Example
10.9 Exercises
10.9.2 The Bilevel or Double Loop Approach for a Desired Objective
10.9 Example
10.9 Example
10.9 Example
10.9 Exercises
Bibliography
Index