Modeling Anticipation

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Bill Braun
Senior Member
Posts: 73
Joined: Fri Mar 29, 2002 3:39 am

Modeling Anticipation

Post by Bill Braun »

Assumption: In an SD model (within the context of a policy) past decisions
are "made present" through feedback from stocks. The stocks capture the
diffusion of decisions over time. The mess that results is the accumulation
of the effects of a stream of decisions, i.e., iterations of Decision >
Flow > State of Stock > Feedback > Decision.

Can forecasts of the future be dynamically modeled, with information from
stocks (that represent a future state) feeding back into current decisions?

I am doing work with projected changes in environmental uncertainty and the
corresponding changes that would be initiated (in the present) to adjust
internal management process so as to be in alignment with the external
environment when the forecast becomes present.

SD models, with which I am familiar, rely on the current state of a stock
to feed information into the current decision, delays contributing to
either (a) the state of the stock as a function of prior decision(s) (lags
in effect) and/or (b) the availability of the information in the stock to
the decision (lags in feedback).

How can this dynamic (described in terms of equations) be reversed
(reversed in the sense that forecasted information from the future state
of a stock flows into current decisions)? How can dynamic forecasts of the
future states of stocks be quantified in models for the purpose of making
present decisions?

I can imagine a table function, for example, with a variable name such as
"forecasted environmental uncertainty five years hence" that is part of the
decision equation. I cannot envision though how the same forecasted
information could be modeled dynamically and be made available to current
decisions.

Bill Braun
From: Bill Braun <medprac@hlthsys.com>
Tom Fiddaman
Senior Member
Posts: 55
Joined: Fri Mar 29, 2002 3:39 am

Modeling Anticipation

Post by Tom Fiddaman »

Bill -

Im going to take Jay Forresters advice and speak in black and white for
those listening in shades of gray, so take this note with a grain of salt.

A frequent approach to forecasting in models is to assume that they are
perfect, by using optimization to make the decision in question. Many
economic models (including those addressing environmental issues) take this
path. Unfortunately, its kind of ridiculous, as it assumes the
decisionmaker has a perfect model of the system, knowledge of the system
state, etc. Its especially ridiculous for environmental models where much
of the point may be that agents in the system are abusing it as a result of
various misperceptions.

All forecasts do involve a model of the system, though. A frequent
"forecast" in SD models (adaptive expectations) is provided by a SMOOTH
function. In this case the model may be that no conscious forecasting is
going on or that the subject of the forecast just happens to be a
stationary random process for which a SMOOTH is a good forecast. The next
step in complexity is to use a SMOOTH to preserve a historical value of a
variable, which then allows trend extrapolation, as in the FORECAST
functions in SD software. Its possible to construct many variations on
this theme - higher orders (2nd derivatives), exponential instead of linear
etc.

However, I suspect that these miss the point youre after. My guess is that
youre dealing with an environmental system for which simple extrapolation
is a poor model, because it has nonlinearities and feedback that create
thresholds or turning points that will be missed by extrapolation. In that
case, what you really want is a model-within-a-model: figure out what real
peoples model of the system is, build it, put it in the context of a
"better" model representing reality, and then feed it some history and
execute it offline (more or less continuously) as the driver for the
decision. Unfortunately, this is hard (but not impossible) to implement in
SD packages Im familiar with, unless you get lucky and can find an
analytical solution to the forecasting problem. If you want a forecast of
uncertainty, not just a best guess, youre in an even tougher pickle, as
this means your model-within-a-model will need to use Monte Carlo simulation.

The reason people dont complain much about the difficulty of implementing
such a system is that there dont seem to be a lot of circumstances where
you can find models in use that are really driving decisions. Even where
the models exist, theres usually a layer of politics, bureaucracy or other
idiocy surrounding the model, which acts on selectively-picked model
results and data that correspond with mental models that look like SMOOTHS.

Tom

****************************************************
Thomas Fiddaman, Ph.D.
Ventana Systems http://www.vensim.com
8105 SE Nelson Road Tel (253) 851-0124
Olalla, WA 98359 Fax (253) 851-0125
Tom@Vensim.com http://home.earthlink.net/~tomfid
****************************************************
paulnewton@attglobal.net
Junior Member
Posts: 7
Joined: Fri Mar 29, 2002 3:39 am

Modeling Anticipation

Post by paulnewton@attglobal.net »

Bill,

Im not an expert, but it strikes me that Chapter 16 of John Stermans
"Business Dynamics" textbook is about just such forecasts as you
describe. See the explanation of the trend function in Section 16.1,
and also the forecast function on page 640.

Why could such forecasts not be used in the current decision-making
structure of a model?

I recently built a model in which I used two such forecasts. In both
cases I used the trend and forecast functions that Sterman describes.
In one part of the model, business unit performance was forecast and
then multiplied by a "stretch" factor to set goals for the performance
of existing capacity. In another part of the model a forecast of
production capacity was used to influence the current capacity ordering
decision.

Hopefully Im on the right track in trying to answer your question.

Paul Newton

Master Phil.Student
University of Bergen (temporarity visiting Cornell University)
paulnewton@StewardshipModeling.com
"Raymond T. Joseph"
Junior Member
Posts: 17
Joined: Fri Mar 29, 2002 3:39 am

Modeling Anticipation

Post by "Raymond T. Joseph" »

I have modeled this as follows:

There are two systems, the system you can control and the system that you
are responding to - the environment. You dont know what the environment is
going to do, but you know the general behavior in terms of its dynamics and
you have some (statistical) concept of its expected behavior. Its expected
behavior has two types of variables. It has unknown parameters of its
inputs and internal components which effect its dynamic behavior. This
requires two tools which need to be coordinated.

The policy design requires an optimization of some objective function over a
specified time horizon. Given the unknown characteristics of the
environmental system component values can be addressed with a method known
as robust control. Given some statistical description of the unknowns, a
statistical description of the required control policy may be developed
which optimizes the response with respect to the objective function. A
control policy can be designed which makes a trade-off between the mean and
variance of a target optimization trajectory. That is, the mean of the
error of tracking the desired trajectory can be lowered at the cost of
increasing the expected variance.

Similar to the above robust control process, the statistical nature of the
inputs to the environment may be addressed by a method called stochastic
control. As above, the statistics of the input parameters are used to
design an optimal control policy that makes a trade-off between the
resultant mean and variance of the tracking error.

Raymond T. Joseph
From: "Raymond T. Joseph" <
rtjoseph@ev1.net>
"Jim Hines"
Senior Member
Posts: 88
Joined: Fri Mar 29, 2002 3:39 am

Modeling Anticipation

Post by "Jim Hines" »

Bill Braun asks
>Can forecasts of the future be dynamically modeled, with information
from >stocks (that represent a future state) feeding back into current
decisions?

The answer is generally "no" in a **model** because using knowledge of a
future state in current decisions will usually affect the future state.
The answer is absolutely "no" in **real world** because no one has
access to information about the future (various prophets, psychics, and
fortune tellers excepted, of course).

Instead, you want to represent the way that people try to get a handle
on the future in the real world. The process always (and only) utilize
past and current information represented as part of the current state of
the system.

If, you **still** want to use information from the future in a model ...
well ... you can, if the (simulated) future is not affected by the
"current" simulation model. You can input time series of the future
(entered via a table function or spreadsheet) or even have a "future"
model run along side the "current" model. (Note, if you do decide to
make future information available to a models policies, youll need to
do some fancy (or fast) talking to engage an SD-savvy audience).

Jim Hines
jhines@mit.edu
=?iso-8859-1?Q?Andr=E9_Reichel?=
Junior Member
Posts: 14
Joined: Fri Mar 29, 2002 3:39 am

Modeling Anticipation

Post by =?iso-8859-1?Q?Andr=E9_Reichel?= »

Bill Braun wrote:

| Can forecasts of the future be dynamically modeled, with information from
| stocks (that represent a future state) feeding back into current
decisions?

Let me get this straight: you ask for a reversed prediction tool. A model
that derives the current state of stocks from their future state. If I dont
miss any point, this appears tautological to me. Either the future state is
a desired (or feared) scenario and you would like to test what kind of
impact it would have on your present management structures and decision
policies; or the future state emerges from your present decisions and you
would like to forecast it. The task that makes most sense for a SD modelling
effort, is to build a model of your pesent management processes and systems
and challenge it with your hypothetic state of the future. Then you can
start to improve processes by adding/changing feedback, alter decision rules
and/or change the structure of your model. All other questions seem a bit
futile to me. And I would heavily suggest not to bring noise in form of a
table function "forecasted environmental uncertainty five years hence" into
the model. The outcome would then be too much dependent on the drawings of
this function.

Viele Grüße

André Reichel
A.Reichel@epost.de
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