Re: COVID and probabilities
Hi Alex,
Le 2025-07-28 00:32, Alex Lieflander a écrit :
Hi Julien,
This will be more relevant later in the email, but I want it at the
top. Your probability calculations are just wrong, and I can show it
with a simple example: Imagine you flip a coin 3 times in a row,
You missed the point again. Here you are still confusing the probability
of doing one same thing three times in a row, and doing the same thing
three times in a single action. For flipping coins it ends up being the
same: flipping 3 coins at once, enumerating outcomes gives all heads
being one out of 8 possible outcomes (hence p=1/8); repeating flipping 1
coin 3 times also gives p = (1/2)^3 = 1/8 for all heads.
But the textbook analogy of catching COVID would be more like drawing
balls from an urn with replacement, with very large numbers of balls;
the urn being the venue space, and the balls ambient air. You can easily
see how the assumption that doing n draws at once is the same as doing n
successive draws doesn't hold there by imagining this experiment: let's
have an urn with 9 black balls and 1 red ball. If you draw 10 balls at
once, emptying the urn (that is, replacing the balls only after the
observation), your probability of not getting the red ball is 0. If you
draw and replace a single ball 10 times, the probability of not getting
a single red ball in these 10 successive draws is p = 0.9 ^ 10 = 0.35.
so by your logic the probability of getting heads at least once in
those 3 flips should be 1x0.5 + 1x0.5 + 1x0.5 = 1.5 or 150%.
No, see above (enumeration). My logic with the previous message was to
keep your hypothesis that the probability for every attendee to catch
the disease from a single unmasked CoV emitter is 0.05. With an urn
initially containing 100 black balls, that would mean removing 5 black
balls from that urn to replace them with red balls. Repeat that for
every CoV emitter you add to the attendance. With enough of them, at
some point all the black balls will be removed, leaving only red balls
in the urn.
Anyway, your argument is based on the *relative* risk between very
similar situations, so a lot of the approximation errors cancel out.
They really don't cancel out and will cumulate to much larger errors if
you use enough of them to estimate probabilities, then use these
probabilities to calculate a relative risk. That was the whole point of
the last message.
If you assume that a person gets infected, then your probabilities for
who it was that infected them are probably correct, but that fails to
take into account that a person is more likely to get infected with
knowingly-positive people who wear a mask instead of self-isolating.
No, that was taken into account in my previous message and the kotlin
code. Sample output with your initial hypotheses:
Model: First model (2025-07-18 22:43:33 +0200)
Without isolation:
New infected attendees: 138
Probability: 0.36316
With isolation:
New infected attendees: 101
Probability: 0.26579
Model: Second model (2025-07-25)
Without isolation:
New infected attendees: 168
Probability: 0.44211
With isolation:
New infected attendees: 114
Probability: 0.30000
If it's reasonably possible that not self-isolating noticeably
increases the risk of people dying when the alternative is
inconvenience, I don't think that's acceptable.
First, isolation is not mere "inconvenience", it's the equivalent of
being banned from the event: an extreme measure. That so many people
here are not realizing this is really concerning. An inconvenience would
be, for example, wearing a mask at all times, and by the way some of
those that complained the loudest were visibly not willing to endure
that inconvenience themselves, even though it would reduce their own
risk by at least two thirds — inconvenience for thee, not for me.
Then I'm pretty convinced that relaxing the currently overreaching
policy will not noticeably increase the risk and might actually even
achieve the reverse, as currently it encourages people to ignore and
hide their symptoms and avoid testing for fear of being excluded from
the event. There must certainly be good reasons that explain why an
overwhelming majority of health authorities around the world relaxed or
dropped their isolation policies.
Cheers,
--
Julien Plissonneau Duquène
Reply to: