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Statistical Challenges in Agent-Based Computational Modeling

Statistical Challenges in Agent-Based Computational Modeling. L ászló Gulyás ( lgulyas@aitia.ai ) AITIA International Inc & Lorand Eötvös University , Budapest. Overview. On Agent-Based Modeling (ABM) Properties, Praise & Critique Example ABMs as Stochastic Processes

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Statistical Challenges in Agent-Based Computational Modeling

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  1. Statistical Challenges in Agent-Based Computational Modeling László Gulyás (lgulyas@aitia.ai) AITIA International Inc& Lorand Eötvös University, Budapest

  2. Overview • On Agent-Based Modeling (ABM) • Properties, Praise & Critique • Example • ABMs as Stochastic Processes • Source of Randomness • Basic ABM Methodology • Verification & Validation • Challenges & Directions • Networks • Example • Experimental Validation • Example • Conclusions Gulyás László

  3. Overview • On Agent-Based Modeling (ABM) • Properties, Praise & Critique • Example • ABMs as Stochastic Processes • Source of Randomness • Basic ABM Methodology • Verification & Validation • Challenges & Directions • Networks • Example • Experimental Validation • Example • Conclusions Gulyás László

  4. On Agent-Based Modeling (ABM) • Main Properties • Bottom-Up • Individuals with their idiosyncrasies, • With their imperfections (e.g., cognitive or computational limitations) • Heterogeneous Populations • Dynamic Populations • Explicit Modeling of Interaction Topologies • Examples • Santa Fe Institute Artificial Stock Market • Discrete Choices on Networks (Social Influence Modeling) Gulyás László

  5. Praise of ABM • Attempt to Create Micro-Macro Links • “Micromotives and Macrobehavior” • Generative Modeling Approach • Realistic Microstructures • Explicit Representation of Agents • Realistic Computational Abilities • Modeling of the Information Flow • Tool for Non-Equilibrium Behavior • Ability to Study Trajectories Gulyás László

  6. Critique of ABM • (Mis)Uses of Computer Simulation • Prediction………………………… (Weather) • “Simulation”……………………..(Wright Bros) • Thought Experiments /………(Evol of Coop.)Existence Proofs • Computational (In)Efficiency • Questionable Results / Foundations? Gulyás László

  7. Overview • On Agent-Based Modeling (ABM) • Properties, Praise & Critique • Example • ABMs as Stochastic Processes • Source of Randomness • Basic ABM Methodology • Verification & Validation • Challenges & Directions • Networks • Example • Experimental Validation • Example • Conclusions Gulyás László

  8. Example I. • The Santa Fe Institute Artificial Stock Market (SFI ASM) (Arthur et al., 1994, 1997) Gulyás László

  9. The Santa Fe Institute Artificial Stock Market (1/3) • A minimalist model of two assets: • “Money”: fixed, risk-free, infinite supply, fixed interest. • “Stock”: unknown, risky behavior, finite supply, varying dividend. • Artificial traders • Developing (learning) trading strategies. • In an attempt to maximize their wealth. Gulyás László

  10. The Santa Fe Institute Artificial Stock Market (2/3) • Trading rules of the agents • Actions (buy, sell, hold) based on market indicators: • Fundamental and Technical Indicators • Price > Fundamental Value, or • Price < 100-period Moving Average, etc. • Reinforced if their ‘advice’ would have yielded profit. • A classifier system. • A Genetic algorithm • Activated in random intervals (individually for each agent). • Replaces 10-20% of weakest the rules. Gulyás László

  11. The Santa Fe Institute Artificial Stock Market (3/3) • Two behavioral regimes (depending on learning speed). • One (Fundamental Trading) – Theory • Consistent with Rational Expectations Equilibrium. • Price follows fundamental value of stock. • Trading volume is low. • Two (Technical/Chartist Trading) – Practice • “Chaotic” market behavior. • “Bubbles” and “crashes”: price oscillates around FV. • Trading volume shows wild oscillations. • “In accordance” with actual market behavior. Gulyás László

  12. Overview • On Agent-Based Modeling (ABM) • Properties, Praise & Critique • Example • ABMs as Stochastic Processes • Source of Randomness • Basic ABM Methodology • Verification & Validation • Challenges & Directions • Networks • Example • Experimental Validation • Example • Conclusions Gulyás László

  13. ABMs as Stochastic Processes • Not modeled processes are typically represented by stochastic elements. • ABMs are implemented as Discrete Time Discrete Event simulations. • Markov Processes • Often with enormous state-spaces… Gulyás László

  14. ABM Methodology (101) • High dimensionality of the parameter space. • Only sampling is possible. • Establishing results’ independence from pseudo-random number sequences. • Sensitivity analysis, wrt. • Parameters • Pseudo-Random Number Sequences Gulyás László

  15. Overview • On Agent-Based Modeling (ABM) • Properties, Praise & Critique • Example • ABMs as Stochastic Processes • Source of Randomness • Basic ABM Methodology • Verification & Validation • Challenges & Directions • Networks • Example • Experimental Validation • Example • Conclusions Gulyás László

  16. Verification & Validation • Challenges • The Challenge of ‘Dimension Collapse’ • ANTs (John H. Miller) • QosCosGrid • EMIL • Empirical Fitting • Micro- and Macro-Level Data • Network Data • Estimation Problems (Endogeneity) Gulyás László

  17. Verification & Validation • Directions I. • Networks • Research on Network Data Collection • Abstract Network Classes • Empirically Grounded Abstract Networks Gulyás László

  18. Example II. • Socio-Dynamic Discrete Choices on Networks in Space (Dugundji & Gulyas, 2002-2006) Gulyás László

  19. Starting Point • Discrete Choice Theory allows prediction based on computed individual choice probabilities for heterogeneous agents’ evaluation of discrete alternatives. • Individual choice probabilities are aggregated for policy forecasting. Gulyás László

  20. Industry Standard in Land Use Transportation Planning Models • Ground-breaking work: • Ben-Akiva (1973); Lerman (1977) • Some operational models: • Wegener (1998, IRPUD – Dortmund) • Anas (1999, MetroSim – New York City) • Hensher (2001, TRESIS – Sydney) • Waddell (2002, UrbanSim – Salt Lake City) Gulyás László

  21. Interdependence of Decision-Makers’ Choices • Discrete Choice Theory is fundamentally grounded in individual choice, however... • Globalversus local versusrandom interactions • Interaction throughcomplex networks • Networkevolution • Problem domain: residential choice behavior and multi-modal transportation planning • Social networks, transportation land use networks Gulyás László

  22. Discrete Choice Model • Population of N decision-making agents indexed (1,...,n,...,N) • Each agent is faced with a single choice among mutually exclusiveelemental alternatives i in the composite choice setC = {C1,...,CM} • For sake of simplicity, we assume that the (composite) choice set does not vary in size or content across agents. Gulyás László

  23. Nested Logit Models m 1 2 ... m ... Mn mLm 12 ... JC112 ... JCm 12 ... JCM Gulyás László

  24. Interaction Effects • We introduce (social) network dynamics by allowing the systematic utilities Vin and Vmn to be linear-in-parameterb first order functions of the proportions xin and xmn of a given decision-maker’s “reference entity” agents making these choices Gulyás László

  25. Empirical Dilemma • In practice… • It can be difficult to reveal the exact details of the relevant network(s) of reference entities influencing the choice of each decision-maker • The actual reference entities for a given decision-maker may not be among those in the data sample • One solution: • studying abstract network classes with an aim towards mathematical understanding of the properties of the model. Gulyás László

  26. Computational Model in RePast Example time series for 100 agents with f(x) = x for (a) low certaintyand (b), (c) high certainty with two distinct random seeds Gulyás László

  27. Results(Random / Erdős-Rényi network) Gulyás László

  28. Results(Watts-Strogatz network) Gulyás László

  29. Empirical Application Socio-Geographic Network

  30. Visualization of Semi-Abstract Socio-Geographic Network Gulyás László

  31. Socio-Geographic Networkb=1.9284, m L=2.5062, Seed 1 Gulyás László

  32. Socio-Geographic Networkb=1.9075, m L=1, Seed 2 Gulyás László

  33. Challenge in Estimation • Endogeneity! Gulyás László

  34. Overview • On Agent-Based Modeling (ABM) • Properties, Praise & Critique • Example • ABMs as Stochastic Processes • Source of Randomness • Basic ABM Methodology • Verification & Validation • Challenges & Directions • Networks • Example • Experimental Validation • Example • Conclusions Gulyás László

  35. Verification & Validation • Directions II. • Experimental Validation • Participatory Simulation • The case of the SFI-ASM Gulyás László

  36. Example III. • The Participatory SFI-ASM (Gulyás, Adamcsek and Kiss, 2003, 2004.) Can agents adapt to external trading strategies, just as well as they did to those developed by fellow agents? Gulyás László

  37. Humans Increase Market Volatility • The presence of human traders increased market volatility. • The higher percentage of the population was human, the higher the difference was w.r.t. the performance of the fully computational population. Gulyás László

  38. Participants Learn Fundamental Trading • First set of Experiments: • Humans initially applied technical trading, but gradually discovered fundamental strategies. • The winning human’s strategy was: • Buy if price < FV, sell otherwise. Gulyás László

  39. Artificial Chartist Agents • Second set of Experiments: • We introduced artificial chartist (technical) agents. • Base experiments show: • Chartist agents normally increase market volatility. • That is, humans are subjected to extreme bubbles and crashes. Gulyás László

  40. Participants Learn Technical Trading • Subjects received a bias towards fundamental indicators. • Still, they reported gradually switching for technical strategies after confronting with the ‘chartist’ market. Gulyás László

  41. Participants Moderate Market Deviations • However, chartist human subjects actually modulated the market’s volatility. • The market actually show REE-like behavior. • The absolute winner’s strategy in this case was a pure technical rule. Gulyás László

  42. Hypothesis • The learning rate again. • The participants may have adapted quicker. • The effect of human ‘impatience’. • Cf. ‘Black Monday’ due to programmed trading. • An apparent lesson: learning agents may do no better. Gulyás László

  43. Overview • On Agent-Based Modeling (ABM) • Properties, Praise & Critique • Example • ABMs as Stochastic Processes • Source of Randomness • Basic ABM Methodology • Verification & Validation • Challenges & Directions • Networks • Example • Experimental Validation • Example • Conclusions Gulyás László

  44. Conclusions • A methodology attempting the micro-macro link: ABM. • Methodological challenges of ABM • Mainly in empirical validation. • Some in parameter space sampling. • Two new directions discussed • Empirical estimation based on semi-abstract networks. • Participatory experiments. Gulyás László

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