Modeling Change and Uncertainty: Machine Learning and Other Techniques
- Length: 446 pages
- Edition: 1
- Language: English
- Publisher: Chapman & Hall
- Publication Date: 2022-07-25
- ISBN-10: 1032062371
- ISBN-13: 9781032062372
- Sales Rank: #0 (See Top 100 Books)
This book offers a problem-solving approach. The authors introduce a problem to help motivate the learning of a particular mathematical modeling topic. The problem provides the issue or what is needed to solve using an appropriate modeling technique.
Cover Half Title Series Page Title Page Copyright Page Contents Preface Authors 1. Perfect Partners: Combining Models of Change and Uncertainty with Technology 1.1 Overview of the Process of Mathematical Modeling 1.2 The Modeling Process 1.2.1 Mathematical Modeling 1.2.2 Models and Real-World Systems 1.2.3 Model Construction 1.3 Illustrative Examples 1.4 Technology 1.4.1 The R© Environment 1.5 Exercises 1.6 Projects References and Suggested Further Reading 2. Modeling Change: Discrete Dynamical Systems (DDS) and Modeling Systems of DDS 2.1 Introduction and Review of Modeling with Discrete Dynamical Systems 2.1.1 Solutions to Discrete Dynamical Systems 2.2 Equilibrium and Stability Values and Long-Term Behavior 2.2.1 Stability and Long-Term Behavior 2.2.2 Relationship to Analytical Solutions 2.2.3 Extending to Squares of Real Numbers Other than Integers 2.2.4 Finding Patterns of Cubes with Discrete Dynamical Systems 2.2.5 Cubes and DDS with Cubes 2.3 Introduction to Systems of Discrete Dynamical Systems 2.3.1 Simple Linear Systems and Analytical Solutions 2.3.2 Analytical Solutions 2.4 Iteration and Graphical Solution 2.5 Modeling of Predator-Prey Model, SIR Model, and Military Models 2.6 Technology Examples for Discrete Dynamical Systems 2.6.1 Excel for Linear and Nonlinear DDS 2.6.2 Maple for Linear and Nonlinear DDS 2.6.2.1 Using Maple for a System of DDS 2.6.3 R for Linear and Nonlinear DDS 2.6.3.1 Logistics Growth 2.7 Exercises 2.8 Projects References 3. Statistical and Probabilistic Models 3.1 Introduction 3.2 Understanding Univariate and Multivariate Data 3.2.1 Displaying the Data 3.2.2 Data Ambiguity 3.2.3 Data Distortion 3.2.4 Data Distraction 3.3 Displays of Data and Statistics 3.3.1 Good Displays of the Data 3.3.2 Displaying Categorical Data - Pie Chart 3.3.2.1 Pie Chart in Excel 3.3.2.2 Pie Chart in R 3.3.2.3 Pie Charts in Maple 3.3.3 Bar Charts for Qualitative Data or Discrete Quantitative Data 3.3.4 Displaying Categorical Data - Bar Chart 3.3.4.1 Bar Charts in R 3.3.4.2 Bar charts in Maple 3.3.5 Displaying Quantitative Data - Stem and Leaf 3.3.5.1 Steam and Leaf Plots in R 3.3.6 Symmetry Issues with Data 3.3.7 Displaying Quantitative Data with Histograms 3.3.7.1 Histogram in R 3.3.7.2 Histogram in Maple 3.3.8 Boxplot 3.3.8.1 Boxplot in R 3.3.8.2 Comparisons with Boxplot (Side by Side) 3.3.8.3 Boxplots in Maple 3.4 Statistical Measures 3.4.1 Central Tendency or Location 3.4.1.1 Describing the Data 3.4.1.2 The Mean 3.4.1.3 The Median 3.4.1.4 The Mode 3.4.2 Measures of Dispersion 3.4.2.1 Variance and Standard Deviation 3.4.3 Measures of Symmetry and Skewness 3.4.3.1 Summary of Descriptive Measures with Excel 3.4.3.2 Descriptive Statistics with R 3.4.3.3 Descriptive Statistics in Maple 3.5 Exercises 3.5.1 Basic Statistics 3.5.2 Statistical Measures References 4. Modeling with Probability 4.1 Classical Probability 4.1.1 The Law of Large Numbers 4.1.2 Probability from Data 4.1.2.1 Intersections and Unions 4.1.2.2 The Addition Rule 4.1.2.3 Complement Rule 4.1.2.4 Conditional Probability 4.1.2.5 Independence 4.1.2.6 Definition of Independent Events 4.2 Bayes' Theorem 4.3 Discrete Distributions in Modeling 4.3.1 Poisson Distribution Poisson 4.4 Continuous Probability Models 4.4.1 Introduction 4.4.2 The Exponential Distribution 4.4.2.1 Exponential Distributions in R 4.4.3 The Normal Distribution 4.4.3.1 Normal Distribution in R 4.4.3.2 Inverse of Normal Distribution 4.4.3.3 Normal Distribution in Maple 4.4.4 Central Limit Theorem 4.4.4.1 The Central Limit Theorem in R 4.5 Confidence Intervals and Hypothesis Testing 4.5.1 Simple Hypothesis Testing 4.5.1.1 Tests with One Sample Mean 4.5.1.2 Tests with a Population Proportion (Large Sample) 4.5.1.3 Tests Comparing Two Sample Means 4.5.2 Notation and Definitions 4.6 Exercises 4.6.1 Classical Probability 4.6.2 Discrete Distributions 4.6.3 Continuous Probability Models 4.6.4 Hypothesis Testing References 5. Differential Equations 5.1 Introduction 5.2 Qualitative Assessment of Autonomous Systems of First-Order Differential Equations 5.2.1 Qualitative Graphical Assessment 5.3 Solving Homogeneous and Non-homogeneous Systems 5.4 Technology Examples for Systems of Ordinary Differential Equations 5.4.1 Excel for System of Ordinary Differential Equations 5.4.2 Maple for System of Ordinary Differential Equations 5.4.2.1 Maple's Use in Nonhomogeneous Systems of Differential Equations for Closed Form Analytical Solutions 5.4.2.2 Part 1: Homogeneous 5.4.2.3 Nonhomogeneous Systems of Differential Equations 5.4.2.4 Phase Portraits 5.4.3 R for System of Ordinary Differential Equations 5.4.3.1 R for Developing Phase Portraits Uses Flow Field 5.5 Exercises 5.6 Projects References and Suggested Future Readings 6. Forecasting with Linear Programming and Machine Learning 6.1 Introduction to Forecasting 6.1.1 Steps in the Modeling Process 6.2 Machine Learning 6.2.1 Data Cleaning and Breakdown of Data 6.2.2 Feature Engineering 6.3 Model Fitting 6.3.1 Simple Least Squares Regression 6.3.2 Exponential Decay Modeling 6.3.3 Linear Regression of Hospital Recovery Data 6.3.4 Quadratic Regression of Hospital Recovery Data 6.3.5 Exponential Decay Modeling of Hospital Recovery Data 6.3.6 Sinusoidal Regression with Demand Data 6.4 Time Series Models 6.4.1 Mean Absolute Percentage Error 6.4.1.1 Formula 6.4.1.2 Notation 6.4.2 MAD 6.4.2.1 Formula 6.4.2.2 Notation 6.4.3 MSD 6.4.3.1 Formula 6.4.3.2 Notation 6.4.4 Exponential Smoothing 6.4.5 Auto-regressive Integrated Moving Average (ARIMA) 6.5 Case Studies of Time Series Data 6.5.1 Time Series with Exponential Smoothing 6.6 Summary and Conclusions References and Suggested Further Readings 7. Stochastic Models and Markov Chains 7.1 Introduction 7.1.1 The Markov Property 7.1.2 Maple for Markov Chains 7.2 Transition Matrices 7.3 Markov Chains and Bayes' Theorem 7.4 Markov Processes 7.5 Exercises Reference 8. Linear Programming 8.1 Introduction 8.2 Formulating Linear Programming Problems 8.2.1 Integer Programming 8.2.2 Nonlinear Programming 8.3 Technology Examples for Linear Programming 8.3.1 Memory Chips for CPUs 8.3.2 Linear Programing in Excel 8.3.3 Excel for Linear Programing 8.3.4 Maple for Linear Programing 8.4 Transportation and Assignment Problems 8.4.1 Transportation Algorithms 8.4.2 Assignment Algorithms 8.5 Case Studies in Linear Programming 8.6 Sensitivity Analysis in Maple 8.6.1 Coefficient of Non-basic Variables 8.6.2 Change of Non-basic Variables Coefficient 8.7 Stochastic Optimization References 9. Simulation of Queuing Models 9.1 Introduction 9.1.1 Simulation Inputs 9.1.2 Simulation Outputs 9.1.2.1 Utilization 9.1.2.2 Number of Customers Waiting 9.1.2.3 Waiting Times 9.1.2.4 Number-of-Customers-in-System 9.1.2.5 Idle Percentage 9.1.3 Other Performance Measures 9.1.4 Determining Capacity 9.1.5 Other Extensions 9.1.6 Summary of Variables and Formulas for Queuing Analysis 9.1.7 Inputs 9.1.8 Outputs 9.1.9 Determining Capacity 9.2 Queueing Model Practice Problems: Solutions 9.2.1 Simulation 9.2.1.1 Algorithm: Missiles 9.2.1.2 Problem Identification Statement 9.2.1.3 Assumptions 9.2.1.4 Model Formulation 9.2.1.5 Algorithm: Inventory 9.2.1.6 Possible Solution with Simulation 9.2.1.7 Algorithm 9.2.2 Maple Applied Simulation 9.2.3 R Applied Simulation 9.3 Exercises 10. Modeling of Financial Analysis 10.1 Introduction 10.1.1 Conjecturing Solutions 10.1.2 Developing a Financial Model Formula 10.2 Simple and Compound Interest 10.2.1 Compound Interest 10.2.2 Continuous Compounding 10.3 Rates of Interest, Discounting, and Depreciation 10.3.1 Annual Percentage Rate (APR) 10.3.1.1 APR for Continuous Compounding 10.3.2 Discounts 10.3.3 Depreciation 10.4 Present Value 10.4.1 Net Present Value and Internal Rate of Return 10.4.1.1 Internal Rate of Return 10.5 Bond, Annuities, and Shrinking Funds 10.5.1 Government Bonds 10.5.2 Annuities 10.5.2.1 Ordinary Annuities 10.5.3 Sinking Funds 10.5.4 Present Value of an Annuity 10.6 Mortgages and Amortization 10.7 Advanced Financial Models 10.7.1 Estimating Growth Rates 10.7.2 Multiple Regression for Sales 10.7.3 Portfolio Optimization 10.7.4 MADM for Project Selection 10.8 Exercises 10.8.1 Compounding Interests 10.8.2 Rate of Interests 10.8.3 Present Value 10.8.4 Mortgages and Amortization 10.9 Projects 11. Reliability Models 11.1 Introduction to Total Conflict (Zero-Sum) Games 11.2 Modeling Component Reliability 11.3 Modeling Series and Parallel Components 11.3.1 Modeling Series Systems 11.3.2 Modeling Parallel Systems (Two Components) 11.4 Modeling Active Redundant Systems 11.5 Modeling Standby Redundant Systems 11.6 Models of Large-Scale Systems 11.7 Exercises Reference 12. Machine Learning and Unconstrained Optimal Process 12.1 Introduction 12.2 The Gradient Method 12.2.1 Gradient Method Algorithm 12.2.2 Gradient Method Algorithm 12.2.3 Training and Test Sets in Machine Learning 12.3 Machine Learning Regression: A Note on Complexity 12.4 Genetic Algorithm as Machine Learning in R 12.5 Initial Population 12.6 Simulated Annealing 12.7 Exercises Reference Index
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