Page 216 - DCAP601_SIMULATION_AND_MODELING

Simulation and Modelling

Notes In the case of the empirical examples sketched above, the case is even simpler. Our model of a
lake and its socioeconomic environment was based on observation, but it would still contain a
number of terms which can only be used within a theory of, say, ecological consciousness:
There would be some link between the state of the lake (its smell or colour) and the state of
ecological consciousness of a particular person living near the lake (something like “the worse
the water smells, the more am I willing to protect the lake from sewage”) and the action this
person takes, and we could only observe the direct link between the observable smell of the lake
and the observable actions taken, so the two “internal” links (as functions with their numerical
coefficients, or as fuzzy rules with their membership functions) would remain theroetical with
respect to such a theory — but the computer programme used for this simulation would still be
a full model of this theory, because it would contain a function or rule representing this link, and
that part of the simulation output which could be compared to empirical observational data
would be the partial potential model of the theory.

Stakeholders, however, might find that the T-theoretical links between the observable state of
the lake and the observable actions on one hand and the T-theoretical state of ecological
consciousness comply with what they think how ecological consciousness (if ever such a thing
exists) works. And this could be the special value simulation could have in participatory
modelling approaches (cf. the last few paragraphs of El hadouaj et al. 2001).
12.3 Analysis for the Design of Simulation Experiments

The traditional (important) methods to design statistical experiments, but rather techniques
that can be used, before a simulation is conducted, to estimate the computational effort required
to obtaindesired statistical precision for contemplated simulation estimators. In doing so, we
represent computational effort by simulation time, and that in turn by either the number of
replicationsor the run length within a single simulation run. We assume that the quantities of
interest will be estimated by sample means. In great generality, the required length of a single
simulation run can be determined by computing the asymptotic variance and the asymptotic
bias of thesample means. Existing theory supports this step for a sample mean of a function of
a Markovprocess. We would prefer to do the calculations directly for the intended simulation
model, but that usually is prevented by model complexity. Thus, as a first step, we usually
approximatethe original model by a related Markovian model that is easier to analyze. For
example,relatively simple diffusion-process approximations to estimate required simulation
run lengthsfor queueing models can often be obtained by heavy-traffic stochastic-process
limits.

Simulations are controlled experiments. Before we can run a simulation program and analyze the
output, we need to choose a simulation model and decide what output to collect; i.e., we need to
design the simulation experiment. Since (stochastic) simulations require statistical analysis of
the output, it is often appropriate to consider the perspective of experimental design.

Example: As in Cochran and Cox (1992), Montgomery (2000) and Wu and Hamada (2000).
Simulations are also explorations. We usually conduct simulations because we want to learn
more about a complex system we inadequately understand. To head in the right direction, we
should have some well-defined goals and questions when we start, but we should expect to
develop new goals and questions as we go along. When we think about experimental design, we
should observe that the time scale for computer simulation experiments tends to be much
shorter than the time scale for the agricultural and medical experiments that led to the theory of
experimental design. With the steadily increasing power of computers, computer simulation
has become a relatively rapid process. After doing one simulation, we can quickly revise it and
conduct others. Therefore, it is almost always best to think of simulation as an iterative process:

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