That's literally the mathematics assuming a sensitivity of 80% with the numbers from the ONS. 159 samples positive in 209,000 tests means minimum possible spec is 99.92%, 80% sensitivity gives you ~99.9947%
Also, that blog doesn't correct for test characteristics properly. The Rogen-Gladen estimator is a better way to do this (although of course still imperfect - Bayesian inference much better if you've got the time)
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This is the point: Sample 340062: false-positive rates of 1.4% if no virus is present Sample 340060 HCoV OC43: false-positive rates of 2.2% (harmless cold corona virus) Sample 340065 HCoV 229E: false-positive rates of 7.6% if present (harmless cold corona virus)
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If your pillar 1 and 2 cases had no COVID at all they could still have higher positives from false positivity arising from cross reactivity with other viruses. The rate could even change over time.
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