This comprehensive guide stands as an invaluable resource for mastering applied systems analysis, engaging both aspiring scientists and those outside the scientific community who have an interest in systems thinking. The book excels in explaining mathematical and statistical techniques, establishing itself as a vital resource for both undergraduate and graduate courses in applied system analysis. Beyond just programming and computation, it offers insights into a variety of problem domains and methodologies relevant to these areas. Its unique combination of theoretical principles and real-world applications, bolstered by empirical examples, equips readers from diverse backgrounds to effectively utilize systems analysis in practical scenarios. In doing so, it equips young scientists and empowers educational institutions around the globe, playing a critical role in shaping curricula and fostering a comprehensive understanding of applied systems analysis.

Acknowledgements
Foreword
Preface

Part 1. Applied Statistics Analysis

1.1. Fundamentals of Statistics - Overview of Statistics, Terminology, Data
1.2. Descriptive Statistics - A Guide to the Concepts of Descriptive Statistics, Distribution, Central Tendency, Variability
1.3. Bell Curve - A Guide to the Concepts of Bell Curve, Empirical Measure of Central Tendency,
Empirical Measure of Dispersion, Central Limit Theorem, Outlier
1.4. Inferential Statistics - A Guide to the Concepts of Inferential Statistics, Sampling for Inference, Hypothesis Testing
- Supplemental Information 1.1: Understanding Research
1.5. Statistical Model, Part 1 - Identification of the t Test, Independent t Test, Independent t Test
Unequal n Two-Tailed, Paired t Test, Factors Affecting the t Test
1.6. Statistical Model, Part 2 - Identification of ANOVA, Two-Way ANOVA, Comparison of One-Way and Two-Way ANOVA
- Supplemental Information 1.2: Experimental Research
- Supplemental Information 1.3: Quasi-Experimental Research
- Supplemental Information 1.4: Qualitative Research
1.7. Statistical Model, Part 3 - Overview of Correlation, Basic Assumptions about Correlation, Facts about Correlation
1.8. Statistical Model, Part 4 - Overview of Simple Regression, Multiple Regression, Logistic Regression
1.9. Statistical Model, Part 5 - Overview of Chi-Square, Chi-Square in Statistics, Chi-Square Test of Independence
- Supplemental Information 1.5: Writing a Research Paper
1.10. Concluding Remarks
- Reading List 1.1: Applied Statistical (Variance-Based) Research Example with Perceptual Accuracy
- Reading List 1.2: Applied Statistical (Regression-Based) Research Example with Executive Function

Part 2. Applied Time Series Analysis

2.1. Fundamentals of Time Series Analysis - Overview of Time Series, A Guide to Stochastic Concepts (4 ways)
2.2. Probability Theory, Part 1 - System Variables, Relative Frequency, Frequency Based Approaches, Probability State Spaces
2.3. Probability Theory, Part 2 - Random Variables, Distributions and Densities, Various Discrete and Continuous Distributions
2.4. Probability Theory, Part 3 - Empirical Probability, Empirical Probability Densities, Moment and Expectation Values
2.5. Probability Theory, Part 4 - Exponential Probability Density, Information Theory, Maximum Likelihood Estimation
- Supplemental Information 2.1: Theoretical Functions of Various Distributions
- Supplemental Information 2.2: Preliminary Requisites for Stochastic Processes
2.6. Stochastic Processes, Part 1 - Definition and Trajectory, Time-Dependent Moments, Joint Probability
2.7. Stochastic Processes, Part 2 - Empirical Detail of Joint Probability, Stationarity, Markov Property
2.8. Markov Chain Modeling, Part 1 - Markov Chains, Marginal vs. Conditional Probability, Practical Practice
2.9. Markov Chain Modeling, Part 2 - Markov Components, Random Walks and Monte Carlo Simulation, Practical Practice
2.10. Stochastic Iterative Maps, Part 1 - Moving Average Model, Autoregressive Model, Practical Practice
2.11. Stochastic Iterative Maps, Part 2 - Autoregressive Moving Average Model, Function and Simulation, Practical Practice
- Supplemental Information 2.3: Autocorrelation
- Supplemental Information 2.4: Power Spectrum
2.12. Master Equations - Identification, Numerical Simulation for Stochastic Systems, Practical Practice
2.13. Markov Diffusion Processes, Part 1 - Dynamics of Markov Diffusion Processes, Wiener Process, Practical Practice
2.14. Markov Diffusion Processes, Part 2 - The Ornstein-Uhlenbeck Process, (Non)Parametric Analysis, Practical Practice
2.15. Concluding Remarks
- Reading List 2.1: Applied Time Series (Probability-Based) Research Example with Elementary
Coordination
- Reading List 2.2: Applied Time Series (Stochastic) Research Example with Modality Dominance

Part 3. Applied Systems Analysis

3.1. Fundamentals of Systems Analysis - Overview of Systems Analysis, Vectors and Scalars, Vector Operation
3.2. Matrices - A Guide to Concepts, Matrix Applications, Implementing Matrices
- Supplemental Information 3.1: Math Symbols with Code
- Supplemental Information 3.2: Differential, Derivative, and Integral
3.3. Networks, Part 1 - A Guide to Concepts, Network Applications, Network Structures,
Measuring Centralities
3.4. Networks, Part 2 - Practical Aspects of Networks, Simulation of Networks Model
- Supplemental Information 3.3: Modules, Packages, and Libraries in Programming
3.5. Agent-Based Model, Part 1 - A Guide to Concepts, Comparing Agent-Based Model to Other Methods, Implementation
3.6. Agent-Based Model, Part 2 - Practical Aspects of Agent-Based Model, Simulations of Agent-Based Model, Cellular Automata
- Supplemental Information 3.4: High Performance Computing (HPC) via Terminals
3.7. Game Theory, Part 1 - A Guide to Concepts, Famous Games and Payoff Matrices, Nash Equilibrium, Prisoner’s Dilemma
3.8. Game Theory, Part 2 - Practical Aspects of Game Theory, Simulation of Game Theory Model
- Supplemental Information 3.5: Systemic Risk Measurement
3.9. Concluding Remarks
- Reading List 3.1: Applied Systems (Agent-Based Simulation) Research with Behavioral Bias
- Reading List 3.2: Applied Systems (Network-Agent Dynamic) Research with Systemic Risk

References
Appendix 1: Statistical Tables
Appendix 2: Glossary of Terms
Appendix 3: Data File Instructions
Appendix 4: Codebook Instructions
Appendix 5: Tables and Figures
Appendix 6: Index