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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


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