How to Make Mathematical Models More Accessible

Mathematical modeling is a fabulous tool for solving problems in almost every field of scientific study, from genetics to astrophysics and everything in between. And yet, so many times the very models that can be of most use to these fields are mysterious black-boxes within which who-knows-what goes on. And sometimes, it must be admitted, the mathematicians behind these models like it this way.

Granted there are many good reasons why, in some cases, complex mathematical models should not be laid bare for anyone and everyone to tinker with and manipulate parameter values and functions. A lot of work goes into the development of advanced models, and the functions and subroutines within are structured with a great deal of care and reason behind them; without an appropriate level of understanding of the both the mathematics and the science behind this functionality, any changes made can have catastrophic consequences for the quality of information coming out of the model results, and may even render them utterly and completely useless. Tinkering for the sake of tinkering is never a justification for changing a well-thought-out model.

However there is no doubt that there are also cases in which the best use of a mathematical model is to lay it bare in front of end-users and give them the ability to change what needs changing - after all, mathematicians cant possibly predict every single vaccination scenario a public health policy-maker might need to evaluate, or every set of conditions a deploying military force might be exposed to. Models with this sort of final intent must be designed from the beginning with this in mind.

User-functionality requires model capabilities that are easy to access, and easy to change. Most often this will apply to mathematical models in simulation (as opposed to pure theoretical) form - frequently presented as editable spreadsheets or free-standing software applications. Thorough user documentation is indispensible in these cases, describing the reasoning behind the original model, the most appropriate areas of the model to be changed, reasonable situations in which these changes might be needed, and just how to go about doing this. Accompanying whitepapers are one option, but the most useable format for user documentation is in the form of interactive (and searchable) help files.

The whole point of user documentation is to help the user, thus it is imperative that this resource be constructed with ease-of-use in mind. This applies to being able to find the topic of interest - and to explaining the issues at-hand not in strictly mathematical terms, but in language appropriate to the individuals intended to be using the model: policy-makers, scientists, strategists, physicians, etc. This can require a great deal of communication skill along with frequent interaction with representatives from these fields to ensure important information is being conveyed accurately. Of course, a well-designed model will most likely have been based on this type of interaction from project inception to coding and debugging, and the development of user documentation should be a logical progression in the process.

But the most essential component in user-documentation of an accessible mathematical model is to clearly lay out the specific conditions and application(s) for which the model was originally designed, and to clarify just how user-directed changes may alter or negate its original intent and accuracy. While users must be aware of how the model works and what they can change, they must also be aware of the consequences of these changes to their results and accept that, though the original model may have been painstakingly validated and tested, its original level of accuracy may no longer apply. Sharing access to the inner workings of models is also sharing risk associated with its alteration - and also the potential reward of finding a previously-unanticipated new application of a great mathematical model. After all, a mathematical model is only useful if its being used.

If your organization has a project that could benefit from a user-editable model, give MathEcology a call - weve got lots of experience in this arena, and wed be happy to help!

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