On Saturday, April 24, 2021 at 2:34:58 AM UTC-4, Bill Sloman wrote:
> On Saturday, April 24, 2021 at 1:20:34 AM UTC+10, Fred Bloggs wrote:
> > On Thursday, April 22, 2021 at 11:42:54 PM UTC-4, Bill Sloman wrote:
> > > On Friday, April 23, 2021 at 7:42:30 AM UTC+10, Fred Bloggs wrote:
> > > > On Sunday, April 18, 2021 at 11:00:20 PM UTC-4, Bill Sloman wrote:
> > > > > On Monday, April 19, 2021 at 1:34:40 AM UTC+10, Fred Bloggs wrote:
> > > > > > "The obscure maths theorem that governs the reliability of Covid testing"
> > > > > >
> > > > > >
https://www.theguardian.com/world/2021/apr/18/obscure-maths-bayes-theorem-reliability-covid-lateral-flow-tests-probability
> > > > > >
> > > > > > He must be getting paid by the word.
> > > > >
> > > > > This explains why Fred is so confused about science. He loses patience with any explanation that covers all the facts he needs to know (and he seems to need to be told rather more of them than most of the rest us ).
> > > >
> > > > There were no facts. He didn't begin to explain Bayes calculation, he just name dropped once and then left it never to return, after trying to wow everyone with that simple conditional probability conversion. Most likely you identify with him because he uses the same approach as you do what with insinuation of deeper understanding and profundity that's just not there, an especially laughable characteristic of your posts, being deliberately vague, insulting his readers and telling them they're wrong.
> >
> > > That's one explanation. The simpler one is that Fred can't understand anything anything even vaguely complicated and blames the writer's poor exposition for the problems created by his own defective comprehension. I've never been able to get him to understand that "highly conserved" doesn't mean "doesn't mutate" but rather that "when it does mutate most of the mutates get selected out rapidly". He'll probably post yet another explanation of why he thinks I'm wrong.
> >
> > More of your pathetically transparent posturing. As usual you're going to shoot your mouth off about anything and everything except the subject at hand. Then you pretend to have some kind of insight into Bayesian statistics but somehow can't begin to scribble the slightest and most elementary calculation because even that much is way over your dimwit abilities.
> Not exactly. I've got to keep the abilities of my audience in mind. As Stephen Hawking famously observed, each additional equation in the text halves the likely readership.
> It wouldn't put off the readers I don't need to address.
> > The little wiki article says it all.
> >
> > P(infected | positive test)= P(positive test | infected) x P(infected)/[P(positive test | infected) x P(infected) + P(positive test | uninfected) x P(uninfected)]
> >
> > In case you can't figure it out, that is the answer to the original question of the article. How likely are you to be infected given a positive test result?
> Not without actual values for probabilities.
> > You're too damn dumb to even understand that little tidbit. And that's just the algebra. You miss the point entirely about P(positive test | infected) and P(positive test | uninfected) are both very rigorously characterized by ongoing statistical sampling fully backed by confirmation testing techniques of extreme precision.
> Sometimes. Useful probabilities are data about the world as it is now, and since you can't take a large number of samples in a very short time you can't get extremely precise data that is up-to-date. Epidemics have a way of changing the real world inconveniently rapidly. And new viral strains make life even more complicated.
The test performance is not one bit a function of time and circumstance, it is very well characterized. If it does deviate, then you're talking about a variant.
> > You can plug in some numbers of well known captured data. In an advanced country:
> > P(positive test | infected) is about 0.99
> > P(positive test | uninfected) is about 0.001 ( according to article example) .> P(infected) runs about 5% in most advanced nations ( other places in can be real bad like 30%)
> > P(uninfected)= 1- P(infected)=95%
>
> That very much depends where you are doing the testing and in which country. The rule is that you should get less than 5% positive outcomes - but all it means is that if you get more than 5% you should be testing more people. In Queensland they recently tested some 28,000 people and didn't get one positive outcome
Didn't I say that in the write-up?! In most of U.S. it is approximately 5%:
"The percentage of COVID-19 RT-PCR tests that are positive (percent positivity) has decreased from the previous week. The 7-day average of percent positivity from tests is now 5.2%. The 7-day average test volume for April 9-April 15, 2021, was 1,189,820, up 1.6% from 1,170,968 for the prior 7 days."
https://www.cdc.gov/coronavirus/2019-ncov/covid-data/covidview/index.html
Right now India is running plus 30%, and that pushes the Bayes estimate to above 99%, effectively 100%. Again making perfect sense because the relative fraction of infected people to the total subpopulation testing positive is overwhelmingly infected. It does show too that a 600% increase in infection rate slows to a 2-point increase in conditional probability, which is a fair desensitization.
> > This makes P(infected | positive test)= 0.99 x 0.05/[0.99 x 0.05 + 0.001 x 0.95]=0.98
> > which answers the original question.
> Incorrectly, in any place that has got the epidemic under control.
Again, you don't understand basic algebra. And you certainly don't know how to interpret
analytic results. You try to fool people by parroting some numbers you've read somewhere, but you can't draw any inference from it because you're too dumb.
For example, if the pandemic is under control to the point of 0% infected, Bayes equation predicts a 0% chance of infection given a positive test result. And that makes perfect sense because no one has it. At the other extreme, if the test has a 0% false alarm rate, Bayes' equation states you have 100% chance of being infected if you get a positive test. And that makes perfect sense since it's impossible for an uninfected person to get a positive result. Your problem with Bayes Rule is you don't understand conditional probability, which is proportionately relative measure, not an absolute one. Another use for Bayes result would be to estimate the infection rate from the P(infected | positive test) data such as it is.
> > You don't like that answer, you can always run the various stats through their 90% confidence intervals to smear it through a range with confidence you're happy with. Good luck with that given your capabilities though.
> I don't like the answer because you've used 5% as the likely level for the proportion of people who really are infected, when correct answer is going to be very context dependent.
Uh-huh, and this without knowing just how the Bayes result is sensitized to infection rate. Brilliant.
> > Notice this has nothing to do with legal interpretation of DNA results or prosecution of murders or any other unrelated trivia.
> >
> > You don't like the idea of thousands of people being falsely told they are positive? Awww.... tough shit!
>
> It doesn't worry me at all. Doing lots of testing is usually a good idea, but it the people tested are told the results of their tests (which isn't a good idea if there are going to be many more false positives than true positives) they do need to be informed about what the test result actually means.
Surveillance testing is not medical diagnostic testing. You're out of touch with all things practical so you don't have anything useful to say about anything. The main reason you're so ignorant is because you think you're too smart to be told anything.
>
> --
> Bill Sloman, Sydney