Page 54 -

48 B. Edmonds

has to run the code—but this just gives one possible outcome from one set of
initial parameters. Thus, there is the problem that the runs one sees might not be
representative of the behaviour in general. With complex systems, it is not easy
to understand how the outcomes arise, even when one knows the full and correct
specification of their processes, so simply knowing the code is not enough. Thus,
with highly complicated processes, where the human mind cannot keep track of the
parts unaided, one has the problem of understanding how these processes unfold in
general.
Where mathematical analysis is not possible, one has to explore the theoretical
properties using simulation—this is the goal of this kind of model. Of course, with
many kinds of simulation, one wants to understand how its mechanisms work, but
here this is the only goal. Thus, this purpose could be seen as more limited than the
others, since some level of understanding the mechanisms is necessary for the other
purposes (except maybe black-box predictive models). However, with this focus on
just the mechanisms, there is an expectation that a more thorough exploration will be
performed—how these mechanisms interact and when they produce different kinds
of outcome.
Thus, the purpose here is to give some more general idea of how a set of
mechanisms work, so that modellers can understand them better when used in
models for other purposes. If the mechanisms and exploration are limited, this would
greatly reduce the usefulness of doing this. General insights are what is wanted here.
In practice, this means a mixture of inspection of data coming from the simula-
tion, experiments and maybe some inference upon or checking of the mechanisms.
In scientific terms, one makes a hypothesis about the working of the simulation—
why some kinds of outcome occur in a given range of conditions—and then tests
that hypothesis using well-directed simulation experiments.
The complete set of simulation outcomes over all possible initialisations (includ-
ing random seeds) does encode the complete behaviour of simulation, but that is
too vast and detailed to be comprehensible. Thus, some general truths covering the
important aspects of the outcomes under a given range of conditions are necessary—
the complete and certain generality established by mathematical analysis might
be infeasible with many complex systems, but we would like something that
approximates this using simulation experiments.
Definition
‘Theoretical exposition’ means discovering then establishing (or refuting) hypotheses about
the general behaviour of a set of mechanisms (using a simulation).

Unpacking some key aspects here:
• One may well spend some time illustrating the discovered hypothesis (especially
if it is novel or surprising), followed by a sensitivity analysis, but the crucial
part is showing these hypotheses are refuted or not by a sequence of simulation
experiments.
• The hypotheses need to be (at least somewhat) general to be useful.