Sunday, December 22, 2013

A thought on computer models

I find people responding to news articles about inferences that people have drawn from large scale computer models, and worry. I have debugged models, and it is hard to do. It is very easy for errors to creep in. Indeed, I spent time early in my career checking a linear programming package that had been supplied to our computer center, finding errors in the code. It is hard enough to check that a large system of equations adequately describes the situation of interest, and that the parameters have been correctly estimated, and correctly entered, without worrying that the solution software will enter its own errors.

Today software packages are more reliable than they were in the bad old days, but I suspect that many of the packages are also far more complex than they were in those days.

Essentially mathematical models extrapolate from basic assumptions. If one assumption is wrong, the extrapolation may well be wrong. A way to protect against wrong assumptions is to do sensitivity analysis, checking to see how sensitive the important results are to each assumption. If the accuracy of specific assumptions is especially important to the credibility of the result, those assumptions can be double and triple checked. But for that to be effective, the modeler has to be aware of all the assumptions in the model, and that is not always true.

Ideally one wants the theory on which a model is based to be correct. Unfortunately, correct theories are not always easy to come by. One possible use of modeling is to extrapolate from known conditions as if the theory is true, and look for situations in which the extrapolation is inaccurate.

An example that bothered me today is from an article in ScienceDaily: Scientists Discover Tipping Point for the Spread of Ideas. The article begins:h
Scientists at Rensselaer Polytechnic Institute have found that when just 10 percent of the population holds an unshakable belief, their belief will always be adopted by the majority of the society.
I would want a very good model, built on very strong theory with at most very modest assumptions, to justify such a sweeping generalization.  I would also want to be sure that the details were right. In this case, however, I doubt on the face of it that the statement is true.

Lets do a  thought experiment. I have been reading The Reformation by Diarmaid MacCulloch, so lets assume that 10 percent of the population has an unshakable belief that the teaching of the Catholic Church is right about the correct practice of Christianity. Let us also assume that 10 percent of the population has an unshakable belief that the position of Martin Luther is right about the correct practice of Christianity.  As the Pope and Luther would both affirm, it is not possible to believe both are correct simultaneously. Thus in this example, the prediction of the ScienceDaily article will not hold; but the article says it will always hold. Woops!

No comments: