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Simulation and Complexity - how they might relate

Simulation and Complexity - how they might relate. Bruce Edmonds Centre for Policy Modelling Manchester Metropolitan University Business School. (Outline). Outline of Talk. A Simple Model of Modelling What Really Happens Consequences of Modelling Complex Phenomena Constraining Our Models

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Simulation and Complexity - how they might relate

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  1. Simulation and Complexity- how they might relate Bruce Edmonds Centre for Policy Modelling Manchester Metropolitan University Business School Simulation and Complexity - how they might relate, Oxford 2003, http://cfpm.org/~bruce slide-1

  2. (Outline) Outline of Talk • A Simple Model of Modelling • What Really Happens • Consequences of Modelling Complex Phenomena • Constraining Our Models • Giving Our Models Meaning • Example Simulations Simulation and Complexity - how they might relate, Oxford 2003, http://cfpm.org/~bruce slide-2

  3. Some ‘Problems’ • Models that are plausible but with little relation to reality, used as conceptual or formal exploration but then projected upon reality • Types of models are confused in terms of use and judgement • Programming is much more accessible than doing mathematics - everyone can build a model and discover something Simulation and Complexity - how they might relate, Oxford 2003, http://cfpm.org/~bruce slide-3

  4. 1. A Simple Model of Modelling Simulation and Complexity - how they might relate, Oxford 2003, http://cfpm.org/~bruce slide-4

  5. known unknown Object System encoding(measurement) decoding(interpretation) input(parameters, initial conditions etc.) output(results) Modelling parts and relations Model (Model of Modelling) Simulation and Complexity - how they might relate, Oxford 2003, http://cfpm.org/~bruce slide-5

  6. Some uses of simulation models • Entertainment • Art • Illustration • Mathematics • Mediation • Design • Science • I.e. helping to understand phenomena Simulation and Complexity - how they might relate, Oxford 2003, http://cfpm.org/~bruce slide-6

  7. Some ‘scientific’ uses of modelling • Prediction • Provide information about a current unknown by inference from known information • Explanation • Provide an explanation why and how an outcome resulted from some conditions • Analogy • Provide a framework for (or a way of) thinking about a poorly understood or complex system (Model of Modelling) Simulation and Complexity - how they might relate, Oxford 2003, http://cfpm.org/~bruce slide-7

  8. Some criteria for judging models • Soundness of design • w.r.t. knowledge of how the object works • w.r.t. tradition in a field • Accuracy (lack of error) • Simplicity (ease in communication, construction, comprehension etc.) • Generality (when you can safely use it) • Sensitivity (relates to goals and object) • Plausibility (of design, process and results) • Cost (time, space etc.) (Model of Modelling) Simulation and Complexity - how they might relate, Oxford 2003, http://cfpm.org/~bruce slide-8

  9. Some modelling trade-offs simplicity generality realism(design reflects observations) Lack of error (accuracy of results) (Model of Modelling) Simulation and Complexity - how they might relate, Oxford 2003, http://cfpm.org/~bruce slide-9

  10. 2. What Really Happens (even in the ‘hard’ sciences) Simulation and Complexity - how they might relate, Oxford 2003, http://cfpm.org/~bruce slide-10

  11. general ‘laws’ and theories explanatory model phenomenological model data model A possible layering of models (by abstraction) the phenomena (What really happens) Simulation and Complexity - how they might relate, Oxford 2003, http://cfpm.org/~bruce slide-11

  12. atomic and chemical laws model of molecule interaction simulation of many molecules measurements A possible layering of models (by granularity and abstraction) the chemical (What really happens) Simulation and Complexity - how they might relate, Oxford 2003, http://cfpm.org/~bruce slide-12

  13. Multiple models • Parallel models • e.g. different models gained by different approaches and simplifications, whose results are compared (e.g. Lasers) • Context-specific models • e.g. quantum models in micro-world and relativistic models in macro-world • Clusters of models • e.g. use of analogical models alongside formal models in atomic physics (What really happens) Simulation and Complexity - how they might relate, Oxford 2003, http://cfpm.org/~bruce slide-13

  14. 3. Consequences of modelling complex phenomena Simulation and Complexity - how they might relate, Oxford 2003, http://cfpm.org/~bruce slide-14

  15. More complex models • Formal models that are too complex for analytic inference to be feasible • simulation models • Complexity and chaos means that the detailed interactions of parts can make a significant difference to results • compound models • What is required is not aggregate results but the detail of processes as they occur • detailed descriptive models (consequences of complexity) Simulation and Complexity - how they might relate, Oxford 2003, http://cfpm.org/~bruce slide-15

  16. Representation of Outcomes Simulation Many views of a model (I)- due to syntactic complexity • Computational ‘distance’ between specification and outcomes means that • There are (at least) two very different views of a simulation Specification (consequences of complexity) Simulation and Complexity - how they might relate, Oxford 2003, http://cfpm.org/~bruce slide-16

  17. Analogy 1 Summary 1 Summary 2 Analogy 2 Theory 1 Representation of Outcomes (I) Specification Theory 2 Representation of Outcomes (II) Simulation Many views of a model (II)- understanding the simulation (consequences of complexity) Simulation and Complexity - how they might relate, Oxford 2003, http://cfpm.org/~bruce slide-17

  18. Models are less general • Each model is of more limited applicability (e.g. a model of this kind of social influence in this situation) • Each model abstracts less from the phenomena (it is more descriptive in nature) • Different models for different purposes (rather than using a single model for all) (consequences of complexity) Simulation and Complexity - how they might relate, Oxford 2003, http://cfpm.org/~bruce slide-18

  19. Many more models • Models at different levels of abstraction • Models at different levels of granularity • Parallel models to check results • Models derived from different ‘views’ • Complementary models covering different situations or contexts • Descriptive models of different instances • Analogical models • Different summaries of collections (consequences of complexity) Simulation and Complexity - how they might relate, Oxford 2003, http://cfpm.org/~bruce slide-19

  20. Example with multiple models (consequences of complexity) Simulation and Complexity - how they might relate, Oxford 2003, http://cfpm.org/~bruce slide-20

  21. 4. Constraining Our Models Simulation and Complexity - how they might relate, Oxford 2003, http://cfpm.org/~bruce slide-21

  22. A priori constraints on models • By what is feasible in terms of cost and time: ‘simplicity’ (e.g. computer simulation) • By the traditions of academic fields (e.g. utility optimising equilibrium models) • By already validated theoretical frameworks (e.g. atomic interaction, Newtonian physics) • By expert and stakeholder opinion • Observation of phenomena (including anecdotal evidence) (constraining models) Simulation and Complexity - how they might relate, Oxford 2003, http://cfpm.org/~bruce slide-22

  23. Post hoc constraints • Accuracy in terms of low error • Consistency and coherence with other models and observations • Of: • Aggregate outcomes • Unfolding of simulation process (detail over time) • Behaviour of component parts (detail over model structure) (constraining models) Simulation and Complexity - how they might relate, Oxford 2003, http://cfpm.org/~bruce slide-23

  24. Constraints on scope • Each layer of the abstraction modelling layer will only be able to safely abstract to a limited extent • Obligation to sketch out the conditions of applicability of simulation models • Abstracting out of the original context risks loosing the meaning of the model • Danger of the use of a model as an interactive analogy due to ‘theoretical spectacles’ effect (constraining models) Simulation and Complexity - how they might relate, Oxford 2003, http://cfpm.org/~bruce slide-24

  25. 5. Giving Our Models Meaning Simulation and Complexity - how they might relate, Oxford 2003, http://cfpm.org/~bruce slide-25

  26. Context • It is impossible to include all relevant causes in any one model (causal spread) • Constant or irrelevant factors can be omitted as long as the conditions under which the model works can be reliably recognised later so it can be applied • Set of all excluded factors can be abstracted to a (modelling) context • Meaning is bootstrapped from reference inside a specific (real) context (Meaning) Simulation and Complexity - how they might relate, Oxford 2003, http://cfpm.org/~bruce slide-26

  27. Semantic complexity • The difficulty of interpreting a rich meaningful domain and descriptions into an impoverished formal model • Establishment of symbol meaning by: • Importing symbols from natural language • Use of symbols in context • Cycle of interaction and learning about symbols (Meaning) Simulation and Complexity - how they might relate, Oxford 2003, http://cfpm.org/~bruce slide-27

  28. The token processing view • That an off-line computation can be viewed as a manipulation of tokens meaningful to humans (by its design) • This contrasts with mapping to world via data models (and measurement) • Model needs to be embedded in interaction with participants in adaptive cycles • All simulation models are somewhat in both ‘worlds’ (Meaning) Simulation and Complexity - how they might relate, Oxford 2003, http://cfpm.org/~bruce slide-28

  29. Object System conceptual model Model Meaning from intermediate abstraction (often implicit) (Meaning) Simulation and Complexity - how they might relate, Oxford 2003, http://cfpm.org/~bruce slide-29

  30. 6. Example Simulations Simulation and Complexity - how they might relate, Oxford 2003, http://cfpm.org/~bruce slide-30

  31. Example 1: a model of social influence and water demand • Investigate the possible impact of social influence between households on patterns of water consumption • Design and detailed behaviour from simulation validated against expert and stakeholder opinion at each stage • Some of the inputs are real data • Characteristics of resulting aggregate time series validated against similar real data (Examples) Simulation and Complexity - how they might relate, Oxford 2003, http://cfpm.org/~bruce slide-31

  32. Example 1: simulation structure (Examples) Simulation and Complexity - how they might relate, Oxford 2003, http://cfpm.org/~bruce slide-32

  33. Example 1: some of the household influence structure (Examples) Simulation and Complexity - how they might relate, Oxford 2003, http://cfpm.org/~bruce slide-33

  34. Example 1: example results (Examples) Simulation and Complexity - how they might relate, Oxford 2003, http://cfpm.org/~bruce slide-34

  35. Example 1: Conclusions • The use of a concrete descriptive simulation model allowed the detailed criticism and, hence, improvement of the model • The inclusion of social influence resulted in aggregate water demand patterns with many of the characteristics of observed demand patterns • The model established how it was possible that processes of mutual social influence could result in widely differing patterns of consumption that were self-reinforcing (Examples) Simulation and Complexity - how they might relate, Oxford 2003, http://cfpm.org/~bruce slide-35

  36. Example 2: integrating domain expertise and aggregate data • Meta-model (or abstract framework) relating a class of consumer preference models to aggregate price and demand time series • Within this marketing practitioner sets, focus brand, key characteristics, values of characteristic for brands (market context) • Within context practitioner investigates the relationship between particular consumer preference models and aggregate results (Examples) Simulation and Complexity - how they might relate, Oxford 2003, http://cfpm.org/~bruce slide-36

  37. Example 2: abstract structure (Examples) Simulation and Complexity - how they might relate, Oxford 2003, http://cfpm.org/~bruce slide-37

  38. Example 2: development cycles (Examples) Simulation and Complexity - how they might relate, Oxford 2003, http://cfpm.org/~bruce slide-38

  39. Example 2: inference and induction of preference models (Examples) Simulation and Complexity - how they might relate, Oxford 2003, http://cfpm.org/~bruce slide-39

  40. Example 2: practitioner or expert specifies: • A list of labels for each of the brands to be considered • A list of labels for each of the relevant product characteristics that are judged to be used by consumers to distinguish between these brands • For each product: • For each characteristic: • A number representing the perceived intensity of that characteristic associated with that brand (Examples) Simulation and Complexity - how they might relate, Oxford 2003, http://cfpm.org/~bruce slide-40

  41. Example 2: a UK market for liquor (Examples) Simulation and Complexity - how they might relate, Oxford 2003, http://cfpm.org/~bruce slide-41

  42. Cluster Relative Price Expensiveness Size Specialness Uniqueness A (21%) 1 7 6 0 B (49%) 1 5 8 5 C (29%) 2 9 3 9 Example 2: preference model (Examples) Simulation and Complexity - how they might relate, Oxford 2003, http://cfpm.org/~bruce slide-42

  43. Example 2: Conclusions • Meta-model designed to be consistent with observations of how people purchased • Iteratively tested on several different markets for alcoholic drink in different countries • Preference models in terms meaningful to practitioner, because: • They set the market context meaningfully • They interacted with the model within this (Examples) Simulation and Complexity - how they might relate, Oxford 2003, http://cfpm.org/~bruce slide-43

  44. ConclusionsDanger of confusing: • Explanatory and predictive models (e.g. economics) • Semantic and syntactic views of a model (e.g. unwarranted imputing meaning on suggestive animations of model results) • Descriptive and generative models (e.g. analytical summaries of collections of data with generative models) (Conclusions) Simulation and Complexity - how they might relate, Oxford 2003, http://cfpm.org/~bruce slide-44

  45. ConclusionsSome uses of simulations: • Making calculation and inference where analytic solutions are not possible • Exploring possibilities • Establishing counter-examples • Informing (and being informed by) good observation of phenomena • Making dynamic formal descriptions (staging abstraction) (Conclusions) Simulation and Complexity - how they might relate, Oxford 2003, http://cfpm.org/~bruce slide-45

  46. “Model 2 Model” workshop • Considering how simulation models might be related to each other • Particularly with respect to modelling social phenomena • To be held at CNRS, Marseilles, 31st March and 1st April 2003 • Deadline for submissions is past but attendance is free, (but tell us you are coming, there may even be free meals) http://cfpm.org/m2m Simulation and Complexity - how they might relate, Oxford 2003, http://cfpm.org/~bruce slide-46

  47. The End Bruce Edmonds bruce.edmonds.name Centre for Policy Modelling cfpm.org Simulation and Complexity - how they might relate, Oxford 2003, http://cfpm.org/~bruce slide-47

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