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*From*: John Denker <jsd@av8n.com>*Date*: Fri, 17 Apr 2020 21:08:12 -0700

Hi Folks --

New document:

https://www.av8n.com/physics/noisy-exp-fit.htm

When an exponential process is producing only a few events, it

requires a bit of skill to model the process. The appropriate

methods are worth learning, because they are quite general.

They could apply to radioactive decay, or to the growth of

yeast in bread or beer, or (!) to the spread of disease in

some local area.

Note that we are long past the stage where you can model the

coronavirus pandemic on a country-by-country basis, or even a

state-by-state basis. There are a squillion different outbreaks,

each busily exponentiating at its own rate.

This creates extra work for folks who are trying to make sense

of the data. In particular, when you look at a local area,

there are very few events to work with. Extracting reliable

estimates of the growth rate is not trivial. There will be

a lot of uncertainty in the extracted parameters.

One thing you cannot get away with in situations like this is

taking the logarithm of the ordinate and fitting a straight

line to it using linear regression. You can appreciated this

by looking at figure 1: Some of the data points are zero. If

you take the logarithm of that, you get minus infinity. You

cannot fit to such points using a straight line. And you

cannot afford to ignore these points. So skip the logarithm

and skip the linear regression, and use the industrial-strength

nonlinear fit.

If you have a greater number of events at each

x-value, you might try the trick of fitting a

straight line on semi-log paper, but even then

you risk introducing bias into the results.

Another thing you cannot get away with is an unweighted fit.

For the next level of detail, including a bunch of diagrams,

see:

https://www.av8n.com/physics/noisy-exp-fit.htm

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