[BlindMath] Bayes' Theorem

Wed Jan 19 03:24:46 UTC 2022

Hello Pranav,

There are only four possible outcomes, two of which involve being tested positive.

The total probability of being tested positive is the sum of the two outcomes that involve being tested positive. The first is that the subject is infected and tests positive, while the second is that they are not infected and test positive.

You end up with a construct of x/(x+y) where x is the outcome of interest and y is the other outcome that is relevant. The questions is linked to being infected while the tested positive has that and the unfortunate false positive.

Perhaps put the four outcomes as true/false positive/negative and see what you get.

HTH
Jonathan

-----Original Message-----
From: BlindMath <blindmath-bounces at nfbnet.org> On Behalf Of Pranav Lal via BlindMath
Sent: Wednesday, 19 January 2022 3:20 PM
To: 'Blind Math list for those interested in mathematics' <blindmath at nfbnet.org>
Cc: pranav.lal at gmail.com
Subject: Re: [BlindMath] Bayes' Theorem

Dear Jonathan,

Your explanation is just what I was looking for.

One request:
The probability of a random person being infected and testing positive is whereas the probability of a random person being clear and still testing positive is  .
The probability that the random person (who has now tested positive) actually is infected is 0.01998 divided by the total probability that they were positive (0.01998+0.0294) is therefore

How are we getting the total probability of the person being positive?
Could you put the equation into words and then put in the numbers?

This is the sort of challenge I have run into with many textbooks where I do not remember where the previous numbers came from so need a refresher of the formula in words. 

May be this is just me.

If I am confusing you, let me know. This is easier to explain with real time audio communication. 
Pranav
-----Original Message-----
From: BlindMath <blindmath-bounces at nfbnet.org> On Behalf Of Jonathan Godfrey via BlindMath
Sent: Monday, January 17, 2022 10:41 AM
To: 'Blind Math list for those interested in mathematics'
<blindmath at nfbnet.org>
Cc: Jonathan Godfrey <A.J.Godfrey at massey.ac.nz>
Subject: [BlindMath] Bayes' Theorem

Hello Pranav and others,

I added an example to the help page for Bayes' Theorem at https://r-resources.massey.ac.nz/help/bayes.html

This is a classic example where the formula overcomplicates the realities of working with simple examples. Even expressing the formula in words makes it uglier than it needs to be.

I haven't used a probability table, but putting the numbers used in my example into a table might make it much easier to see what is happening.

Hope this helps,
Jonathan

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