[nudephil (OP)]

Dave sent in the following:

I'm interested in how the infection rates are estimated.

• Given that only a small percentage of the population will be tested over any particular period how can the results of these test results be extrapolated to represent the population as a whole?
• Also to be considered is that we are only asked to request a test if symptoms are present. Does this skew the results and if so how?
• Are all test results included or just those undertaken each week?
• Is any account taken of people having multiple tests within the analysis period and the impact this would have on estimated infection rate?

Any insight?

[alancalverd]

If you test a large random sample of the population you will get a crude infection rate and also an idea of the ratio ρ of asymptomatic to symptomatic carriers. You can then multiply the national number of known tested positives by
(ρ + 1) to get the lower bound of probable total infectees, assuming that most of those who volunteer for testing are symptomatic.

The only certain fact is that any "experimental"  number will be an underestimate because the infection is spreading. It's a bit like the absurd journalistic cliche "the death toll is rising" - it can't go down,dear!

[Bored chemist]

Given that only a small percentage of the population will be tested over any particular period how can the results of these test results be extrapolated to represent the population as a whole

Quite well, as long as infection isn't too rare.
To a rough approximation the error margin on counting random things like "people with infections" has a standard deviation of the square root of the number you count.

So, if you test enough people to get 100 with covid then you get the ratio of people with/ people without correct to about 1 in 10 (measured as a relative SD) and about 1 in 5 at the 2 sigma level.
Knowing the infection rate +/- 20% is probably good enough most of the time.

To a depressingly good approximation, you can also measure the rate once and then assume that the number of new cases each week is proportional to the number of current cases- i.e. you can assume that the famous "R" value is constant.