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Complexity and Scientific Modelling

8 Complexity and Induction

From this framework it is clear that a lack of complexity is, in general, not a reliable guide to a model's error rate
*1, unless the problem and modelling language happen to be constructed that way*2. On the other hand experience has frequently shown us that the less complex theory often turns out to be more useful. The answer to this riddle becomes clear when one takes into account the process whereby models are typically developed.

An ideal modeller without significant resource restrictions might well be able to attempt a fairly global search through possible model forms. Some automatic machine-based systems approximate this situation and there it does indeed seem to be the case then that a lack of complexity is no guide to truth (e.g. [13]) - in fact, if anything the reverse seems to be true since there are typically many more complex expressions than simpler ones.

Usually, however, and certainly in the case of human modellers they do not have this luxury. They can check only a very limited number of the possible model forms. Fortunately, it is frequently the case that the meaning of the models allows us to intelligently develop and combine the models we have, to produce new models that are much more likely to produce something useful than a typical automatic procedure. Thus it is frequently the case that it is sensible to try elaborations of known models first before launching off into unknown territory where success is, at best, extremely uncertain.

On its own elaboration is, of course, an inadequate strategy. One can get into a position of diminishing returns where each elaboration brings decreasing improvements in the error rate, but at increasing cost. At some stage preferring simpler and more radically different models will be more effective. Thus sometimes choosing the simpler model, even if less precise and accurate is a sensible heuristic, but this is only so given our knowledge of the process of theory elaboration that frequently occurs.

Complexity and Scientific Modelling - 04 APR 97
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