Model to Model Workshop, EHESS, Grequam/CNRS, Marseille 2003, http://cfpm.org/m2m slide-1

Model ModelWorkshop

- relating simulation models

At EHESS, GREQUAM/CNRS

Marseille, 2003

Welcome to the…

Model to Model Workshop, EHESS, Grequam/CNRS, Marseille 2003, http://cfpm.org/m2m slide-2

Organisation

Juliette Rouchier

durandal.cnrs-mrs.fr/GREQAM/cv/rouchier.htm

David Hales

www.davidhales.com

Bruce Edmonds

bruce.edmonds.name

EHESS, GREQUAM/CNRS

durandal.cnrs-mrs.fr/ehess/ehess.html

Centre for Policy Modellingcfpm.org

Model to Model Workshop, EHESS, Grequam/CNRS, Marseille 2003, http://cfpm.org/m2m slide-3

Relating Models- an overview

Bruce Edmonds(including material from David Hales

and Juliette Rouchier)

Model to Model Workshop, EHESS, Grequam/CNRS, Marseille 2003, http://cfpm.org/m2m slide-4

Outline

1. Kinds of model, in particular comparing equation-based modelling and individual/agent-based simulation

2. Some basic ways in which models may be related or compared

3. Some uses for relating or comparing models

Model to Model Workshop, EHESS, Grequam/CNRS, Marseille 2003, http://cfpm.org/m2m slide-5

Part 1: Overview and Comparison of Equation-based Modelling and

Agent-based Simulation

Model to Model Workshop, EHESS, Grequam/CNRS, Marseille 2003, http://cfpm.org/m2m slide-6

Equation-based modellingModel Target Equation-based Model

Actual Outcomes

AggregatedActual Outcomes

AggregatedModel Outcomes

Model to Model Workshop, EHESS, Grequam/CNRS, Marseille 2003, http://cfpm.org/m2m slide-7

Properties of (equation-based) Mathematical Models

• Long tradition, many techniques/results

• Central use of numbers and proof

• In simple cases can derive closed-form (i.e. general) conclusions

• Essentially about states– Atemporal (where time occurs it is reified)– Inference can works in may ways

• Assumptions necessary to represent world

• ‘Art’ of approximation and application

Model to Model Workshop, EHESS, Grequam/CNRS, Marseille 2003, http://cfpm.org/m2m slide-8

Individual-based simulation

Model Target Agent-based Model

Actual Outcomes Model Outcomes

AggregatedActual Outcomes

AggregatedModel Outcomes

Agent-based

Model to Model Workshop, EHESS, Grequam/CNRS, Marseille 2003, http://cfpm.org/m2m slide-9

Properties of (agent/individual-based) Simulations

• Short tradition, fewer techniques/results• Central use of algorithms and computation• Difficult to derive general conclusions

– More like an experiment than an inference

• Essentially about process– Temporal directionality– Process of unfolding observable

• More representational in practice– In time and in composition

• More suggestive of interpretation

Model to Model Workshop, EHESS, Grequam/CNRS, Marseille 2003, http://cfpm.org/m2m slide-10

Some Uses of Mathematics

• To predict what is currently unknown• To explain what is already known• To derive/infer conclusions from axioms• To represent observed phenomena• To explore unobserved possibilities• To make an idea unambiguous• To compress a representation• To show one model is a special case of

another• To construct a formal framework/language

Model to Model Workshop, EHESS, Grequam/CNRS, Marseille 2003, http://cfpm.org/m2m slide-11

Some Uses of Simulation

• To predict what is currently unknown• To explain what is already known• To calculate outcomes from initial set-up• To represent observed phenomena• To explore unobserved possibilities• To make an idea unambiguous• To compress a representation (in theory)• To show one model is a special case of

another (in theory)• To construct a formal framework/language

Model to Model Workshop, EHESS, Grequam/CNRS, Marseille 2003, http://cfpm.org/m2m slide-12

Part 2: Some Ways in which Models may be

Compared or Related

Model to Model Workshop, EHESS, Grequam/CNRS, Marseille 2003, http://cfpm.org/m2m slide-13

A diagram for a simulation model

Code

Agents

Setting

Outcomes from one run

Model to Model Workshop, EHESS, Grequam/CNRS, Marseille 2003, http://cfpm.org/m2m slide-14

As a Summary/Abstraction of Another Model’s Results

• Modelling model results• More abstract model can be of any kind (including

simulations and equation-based models)• Can be a tactic to help understand/analyse complex

models

Model to Model Workshop, EHESS, Grequam/CNRS, Marseille 2003, http://cfpm.org/m2m slide-15

As a Generalisation/Specialisation of Another Model

Model to Model Workshop, EHESS, Grequam/CNRS, Marseille 2003, http://cfpm.org/m2m slide-16

As a Controlled Experiment/Comparison

?

Model to Model Workshop, EHESS, Grequam/CNRS, Marseille 2003, http://cfpm.org/m2m slide-17

Summary of Some Basic Kinds of Model Relation/Comparison

• Abstraction/approximation of another model

• Super/subset of another model

• As a Controlled Comparison

• The code of one model is a component of the code of another

• Others … ?

Model to Model Workshop, EHESS, Grequam/CNRS, Marseille 2003, http://cfpm.org/m2m slide-18

Part 3: Some Uses for Relating Models

Model to Model Workshop, EHESS, Grequam/CNRS, Marseille 2003, http://cfpm.org/m2m slide-19

To check models are equivalent

• Examination of the code suggests a hypothesis that the simulations are equivalent but…

• …this can only be disconfirmed by experiment• Repeated failure to disconfirm hypothesis can lead one to

rely on it• Reveal hidden assumptions – understand the limits of our

creations!

Model to Model Workshop, EHESS, Grequam/CNRS, Marseille 2003, http://cfpm.org/m2m slide-20

As a tool for staging abstraction

Observations of the

phenomena

Descriptive simulation

Equation-based models

Model to Model Workshop, EHESS, Grequam/CNRS, Marseille 2003, http://cfpm.org/m2m slide-21

Comparison to Inform Generalisation

comparison

GeneralisedModel

Model to Model Workshop, EHESS, Grequam/CNRS, Marseille 2003, http://cfpm.org/m2m slide-22

Summary of Some Uses of Relating Models• Check if models are the same

• To reveal assumptions

• As a tool for staging abstraction

• To inform generalisation

• Communicate and compare complex phenomena between researchers

• And … ?