Re: [Swarm-Modelling] foundation of ABMs

[Darren Schreiber]

You raise some interesting questions that go to the heart of the 
epistemological challeng with ABMs.

Here is the very quick version of my thinking.

1)  There are lots of different kinds of ways to evaluate a model.  (A 
paper that I read from the engineering literature on validation 
catalogues 23, but there are many more, I'm sure).

2)  There are many different reasons that you want to evaluate a model.

3)  Items 1 & 2 are, or at least, should be, highly inter-related.  You 
should choose the methods (note that I use the plural, because you 
probably want multiple methods) for evaluation (1) based upon your 
reasons for evaluating the model (2).

"Convergence to some solution" does not make sense for many of the 
problems that I am interested in as a political scientist.  It looks 
like progress is being made in Iraq right now, but I wouldn't contend 
that this real world phenomena will "converge" or that there is "some 
solution."  The social world, just isn't like that.  And, there are 
deep problems with an ontology that constructs the world as having 
point solutions, equilibrium, etc.  For instance, economics wanders 
into moral quagmires when it suggests that everything will reach 
equilibrium.  Empirically, there are reasons to believe that this is 
not true.  Normatively, lots of people may suffer while we wait for a 
social system to converge.

I saw an interesting talk on this by Brian Skryms recently on some work 
he's done with Robin Pemantle (a mathematician friend of mine).  They 
gave an example of the stag hunt problem that can be demonstrated to 
converge mathematically.  However, in extremely long time periods 
(millions and millions of iterations) the problem doesn't converge.

So what kind of conclusions would we draw from a mathematical 
convergence and a lack of computational convergence?  For problems 
where people might suffer and die due to policy choices that are made 
based upon our models, this actually matters a lot.

I have a paper that I would be glad to send out to those interested 
that argues for a four part ontology (theory - model - phenomena - 
noumena) and then takes this ontology to organize the various methods 
we might use for evaluating a model.

The Ontology
Theory -- the ideas that we have in our heads about how the world works
Models -- a specification of the ideas we have in a tangible form (e.g 
a mathematical model, a computer simulation, a narrative in a book 
chapter, etc.)
Phenomena -- the observations we make of the world
Noumena -- the world as it truly is

Typology of Model Evaluation
Theory - Model tests:  face validity, narrative validity, Turing tests, 
surprise tests, etc.
Model - Model tests:  docking, mathematical convergence, analytic 
proofs, etc.
Model - Phenomena tests:  historic data validity, predictive data 
validity, out of sample forecasts, experimental validity, event 
validity
Theory - Model - Phenomena tests (aka robustness):  extreme bounds 
analysis, global sensitivity analysis, automated non-linear testing 
system, validating substructures, degenerate tests, traces, animation 
tests

"Rigor" means very different things to different people.  I dare you to 
fly on a plane that has only been evaluated with analytic proof.  Or, 
to take a drug that only passes the face validity test.  Or, to 
forecast your return on investment using only historic data.

I agree that we have a big epistemological problem in agent-based 
modeling.  The good news is that we have lots of many interesting ways 
of solving it.  The even better news is that serious thinking about the 
big epistemological problems in ABMs should cause other fields to 
re-evaluate the often ad-hoc standards used to define rigor in their 
disciplines.  And the great news is that I think this re-evaluation 
promises a truly "new kind of science" if we seriously consider 
integrating empirical and theoretic concerns with the normative 
motivations that can inform our research.

        Darren



On Apr 5, 2005, at 2:07 PM, Pablo Gomez Mourelo wrote:

> Dear all:
>
> I am an engineer very  interested in agent-based modelling. I have a 
> question for you all, related to justification/foundation of ABMs.
> I have already read some literature and it seems to me that a 
> justification of agent-based modelling has not been achieved (Volker 
> Grimm).
> One of the problems of AB-modelling is that randomness is nearly 
> always included in our simulations, so different executions turn into 
> different outcomes.
> In comparison to mathematical models , it seems to me very difficult 
> to develop a general theory (foundation) of agent based modelling. HOw 
> do we know an ABM converges to some solution? How can we describe 
> stability of an ABM?  Many modellers feel satisfied with the graphical 
> output, but mathematicians always complain about the lack or rigour 
> beneath the simulation.
>
>
> My main question is: does anyone know of any paper/book giving a 
> mathematical foundation of ABMs?
>
> All the best,
>
> --
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> Pablo Gómez Mourelo
> Departamento de Matemática Aplicada
> ETSI Industriales
> C/ Jose Gutierrez Abascal, 2
> 28006 MADRID
> SPAIN
> Universidad Politécnica de Madrid
> Phone: +34 91 336 3105
> Fax:   +34 91 336 3001
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