Extrapolations: reasonable or useless?

Whenever you look at a graph there is a tendency to see trends. Then you extrapolate into the future by extending the curve. To a mathematician this practice is extremely suspect. For example look at the following curve:

What is going to happen next? Well your guess is as good as mine! But as a mathematician, I can tell you that there are very very few curves where past behavior absolutely determines  future behavior! Pretty much every time you use previous data to extrapolate future behavior, you are making lots  of assumptions, any or all of which could turn out to be false. So how can you know if an extrapolation is at least reasonable? (And always remember, you can never know if it true.)

While it isn’t sufficient it is absolutely necessary that extrapolations show their assumptions. If they don’t make those clear, don’t pay attention to them. Ideally they should show multiple curves depending on different  assumptions. For example, the well known IHME projections (https://covid19.healthdata.org/united-states-of-america) show three different assumptions in their projections.

Next keep in mind that any extrapolation first depends on “fitting” a curve to a bunch of points using data from the past. The assumption of what curve is the best fit to existing data depends on what model you are using. Choose the wrong model and the beautiful curve that so captures the past data is completely useless for extrapolations. The most dramatic example of this was the crazy prediction that Covid 19 would vanish by May 15 which used a stock model built into Excel called the ”cubic” model (https://www.vox.com/2020/5/8/21250641/kevin-hassett-cubic-model-smoothing) But even the extrapolations made by the IHME in the early days of the pandemic were plagued by bad assumptions. Of course, being good scientists, they are constantly updating their assumptions and trying to make their curve fitting better predict the future.

But just like short term weather forecasts are much better than long term forecasts, there is one exception to the vast uncertainty that extrapolations carry – it’s when you are dealing with a virus with a known incubation period. In our case, what is going to happen to us in the next two weeks is pretty much set in stone. Even if we locked down the whole country tomorrow, the deaths and new cases over the next two weeks won’t change much from what you can predict based on existing cases and current growth rates.

And unfortunately, it looks to me like Fauci’s prediction of 100,000 cases soon, is going to be way too optimistic. Given we have 70,000+ daily cases now, I think within the next few weeks, we will exceed 125,000 cases. And two weeks after that, it is likely, death rates will also start hitting records.