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,
--
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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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