Many real-life systems are dynamic, evolving, and intertwined. Examples of such systems displaying 'complexity', can be found in a wide variety of contexts ranging from economics to biology, to the environmental and physical sciences. The study of complex systems involves analysis and interpretation of vast quantities of data, which necessitates the application of many classical and modern tools and techniques from statistics, network science, Machine Learning, and agent-based modelling. Drawing from the latest research, this self-contained and pedagogical text describes some of the most important and widely used methods, emphasising both empirical and theoretical approaches. More broadly, this book provides an accessible guide to a data-driven toolkit for scientists, engineers, and social scientists who require effective analysis of large quantities of data, whether that be related to social networks, financial markets, economies or other types of complex systems.
In order to develop the empirical apparatus, we first provide an introduction to probability and statistics, covering both classical and Bayesian statistics (Chapter 2). We go through a discussion of the classical approach to probability and develop the concept of statistical estimation and hypothesis testing, leading to a discussion of Bayesian models. Then we discuss time series models to analyze evolving systems (Chapter 3). In particular, we develop ideas to model stationary and non-stationary systems. Additionally, we review some ideas from financial econometrics that have proved to be very useful for modeling time-varying conditional second moment: that is, volatility. In the next part of the book, we review Machine Learning techniques emphasizing numerical, spectral, and statistical approaches to Machine Learning (Chapter 4). Then we discuss network theory as a useful way to think about interconnected systems (Chapter 5). These four components constitute the building blocks of the Data Science approaches to complex systems.
Author(s): Anindya S. Chakrabarti, K. Shuvo Bakar, Anirban Chakraborti
Publisher: Cambridge University Press
Year: 2023
Language: English
Pages: 305
Part I Introduction
1 Facets of Complex Systems 3
1.1 Features of Complex Systems 6
1.2 A Data-Driven View of Complexity 8
1.3 A World of Simulations 9
Part II Heterogeneity and Dependence
2 Quantifying Heterogeneity: Classical and Bayesian Statistics 15
2.1 Data Characteristics 16
2.2 Probability Distributions 22
2.3 Classical Statistical Inference 41
2.4 Bayesian Statistics and Inference 70
2.5 Multivariate Statistics 81
2.6 Taking Stock and Further Reading 86
3 Statistical Analyses of Time-Varying Phenomena 88
3.1 Some Basic Definitions and Constructions 90
3.2 Stationary Time Series 94
3.3 Analyses of Non-stationary Time Series 114
3.4 Modeling Fluctuations 118
3.5 Scaling and Long Memory 122
3.6 Taking Stock and Further Reading 129
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Part III Patterns and Interlinkages
4 Pattern Recognition in Complex Systems: Machine Learning 133
4.1 Patterns in the Data 133
4.2 Types of Learning Models 134
4.3 Modeling Dependence via Regression 136
4.4 Low-Dimensional Projection 142
4.5 Finding Similarity in Data 152
4.6 Classifying Observations 159
4.7 Model Validation and Performance 172
4.8 Taking Stock and Further Reading 177
5 Interlinkages and Heterogeneity: Network Theory 179
5.1 Understanding Linkages 179
5.2 Parts of a Network 182
5.3 Node- and Network-Level Characteristics 186
5.4 Information Content and Filtered Networks 204
5.5 Influence of Nodes and Edges 208
5.6 Multiple Layers of Connectivity 214
5.7 Communities and How to Detect Them 216
5.8 Network Architectures 222
5.9 Taking Stock and Further Reading 232
Part IV Emergence: From Micro to Macro
6 Interaction and Emergence: Agent-Based Models 237
6.1 Social Segregation: Interactions on Grids 238
6.2 Ripples on Sand-Piles: Self-Organized Criticality 239
6.3 Size of Cities: Scaling Behavior 242
6.4 Inequality and Heterogeneity: Kinetic Exchange Models 248
6.5 Dynamics of Languages: Competition and Dominance 253
6.6 Emergence of Coordination and Anti-coordination: Bounded
Rationality and Repeated Interactions 257
6.7 Realism vs. Generalizability 263
Epilogue 268
References 271
Index 292
