RE: [Swarm-Modelling] foundation of ABMs

[Christopher J. Mackie]

Hi Darren; What's the value-added of 'noumena' in your scheme?  I see it in 
your ontology but not in your typology, and if all we can see is all we can 
see, what role can/do noumena play? 

--Chris

-----Original Message-----
From: address@hidden [mailto:address@hidden On Behalf Of Darren Schreiber
Sent: Tuesday, April 05, 2005 4:11 PM
To: Swarm Modelling
Subject: Re: [Swarm-Modelling] foundation of ABMs


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,
>
> -- 
> +=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=
> 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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>
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