Simulation and Complexity - how they might relate, Oxford 2003, bruce slide-1 Simulation and Complexity - how they might relate Bruce

Simulation and Complexity - how they might relate, Oxford 2003, http://cfpm.org/~bruce slide-1

Simulation and Complexity- how they might relate

Bruce EdmondsCentre for Policy Modelling

Manchester Metropolitan University Business School


Outline of Talk

1. A Simple Model of Modelling

2. What Really Happens

3. Consequences of Modelling Complex Phenomena

4. Constraining Our Models

5. Giving Our Models Meaning

6. Example Simulations

(Outline)


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


1. A Simple Model of Modelling


Modelling parts and relations

(Model of Modelling)

Object Systemknown unknown

Modelinput

(parameters, initial conditions etc.)

output(results)

encoding(measurement)

decoding(interpretation)


Some uses of simulation models

• Entertainment• Art• Illustration• Mathematics• Mediation• Design• Science

– I.e. helping to understand phenomena


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



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.)



Some modelling trade-offs

simplicity

generality

Lack of error (accuracy of results)

realism(design reflects observations)



2. What Really Happens (even in the ‘hard’ sciences)


A possible layering of models (by abstraction)

(What really happens)

the phenomena

data model

phenomenological model

explanatory model

general ‘laws’ and theories


A possible layering of models (by granularity and abstraction)


the chemical

measurements

simulation of many molecules

model of molecule interaction

atomic and chemical laws


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



3. Consequences of modelling complex phenomena


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)


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


Simulation

Representation of OutcomesSpecification


Representation of Outcomes (II)

Many views of a model (II)- understanding the simulation


Simulation

Representation of Outcomes (I)Specification

Analogy 1

Analogy 2

Theory 1

Theory 2

Summary 1 Summary 2


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)



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)


Example with multiple models



4. Constraining Our Models


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)


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)



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



5. Giving Our Models Meaning


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)


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)


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)


Meaning from intermediate abstraction (often implicit)

Object System

conceptual model

Model

(Meaning)


6. Example Simulations


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)


Example 1: simulation structure

• Activity

• Frequency

• Volume Households

Policy

Agent

• Temperature

• Rainfall

• Daylight

Ground

Aggregate Demand

• Activity

• Frequency

• Volume Households

Policy

Agent

• Temperature

• Rainfall

•

Ground

Aggregate Demand

(Examples)


Example 1: some of the household influence structure

- Global Biased- Locally Biased- Self Biased (Examples)


Example 1: example results

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Simulation Date

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eman

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(Examples)


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)


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)


Example 2: abstract structure

Generic Framework

Market Context

Preference Model Preference Model

Preference Model

Market Context

Preference Model Preference Model

Preference Model

(Examples)


Example 2: development cycles

Generic Framework

Market Context

Preference Model

Try new model

Try new context

Try new framework

(Examples)


Example 2: inference and induction of preference models

Generic framework relates a general class of consumer preference models to the data

Aggregate data

All possible models

Market context

specified by practioner

automatic induction

calculation

(Examples)


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)


0

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0 10 20 30 40 50 60 70 80 90 100Weeks

Mar

ket

Sh

are

In-sample Data Out-of-sample Data

Example 2: a UK market for liquor

(Examples)


Example 2: preference model

Cluster Relative Price

Expensiveness Size Specialn

essUniquen

ess

A (21%) 1 7 6 0

B (49%) 1 5 8 5

C (29%) 2 9 3 9

(Examples)


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)


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)


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)


“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


The End

Bruce Edmonds

bruce.edmonds.name

Centre for Policy Modelling

cfpm.org

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Simulation and Complexity - how they might relate, Oxford 2003, bruce slide-1 Simulation and Complexity - how they might relate Bruce