For Magsj: Bayes Theorem and Why It's Relevant

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For Magsj: Bayes Theorem and Why It's Relevant

Postby Flannel Jesus » Sun Jul 17, 2022 4:22 pm

Imagine, for a moment, that you're a doctor. A woman has come in and asked to be given a test for breast cancer. Now your hospital has 2 types of tests in stock - an expensive, incredibly reliable one, and a cheaper one that's far less reliable. Your hospital only has 100 of the expensive test in stock, so your hospital has a policy of rationing out the expensive test, so you give the woman the cheaper test first.

And she tests positive.

As a doctor, it's your job not to just inform her of the results of the test, but specifically what the result means. Now, you know that your test is not 100% reliable - you've given her the cheaper test. You know the following things about the cheaper test:

1% of women who take the test do in fact have breast cancer.
Of the women who do have breast cancer, 80% will get a positive result from this test, 20% negative.
Of the women who do not have breast cancer, 9.6% will get a false positive result from this test, and 90.4% of them will get a negative result.

What do you think her probability of having cancer his, after getting a positive result from this test?

Don't worry about getting the answer wrong - literally 85% of doctors also get it wrong. What does your intuition tell you?
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Re: For Magsj: Bayes Theorem and Why It's Relevant

Postby Motor Daddy » Sun Jul 17, 2022 4:46 pm

Flannel Jesus wrote:
1% of women who take the test do in fact have breast cancer.


She has a 1% chance of having breast cancer, because she took the test.

The real question is: if she DIDN'T take the test what are her chances of having breast cancer?

Let's have a look:


https://www.cancer.org/cancer/breast-ca ... %20disease.

Overall, the average risk of a woman in the United States developing breast cancer sometime in her life is about 13%. This means there is a 1 in 8 chance she will develop breast cancer. This also means there is a 7 in 8 chance she will never have the disease.


Moral of the story: You can decrease your chances of having breast cancer from 13% to 1% just by taking the test! LOL
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Re: For Magsj: Bayes Theorem and Why It's Relevant

Postby Ichthus77 » Sun Jul 17, 2022 4:49 pm

My intuition?

They make money off tests & unnecessary procedures. They slowly kill ignorant people with same. If further testing requires flesh, flip them off, test again later elsewhere, lo’ & behold, they find nothing.

Also true of dentists.

Be okay with death.

Hit reset if they mandate bull****.
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Re: For Magsj: Bayes Theorem and Why It's Relevant

Postby MagsJ » Tue Aug 16, 2022 1:38 pm

Flannel Jesus wrote:Imagine, for a moment, that you're a doctor. A woman has come in and asked to be given a test for breast cancer. Now your hospital has 2 types of tests in stock - an expensive, incredibly reliable one, and a cheaper one that's far less reliable. Your hospital only has 100 of the expensive test in stock, so your hospital has a policy of rationing out the expensive test, so you give the woman the cheaper test first.

And she tests positive.

As a doctor, it's your job not to just inform her of the results of the test, but specifically what the result means. Now, you know that your test is not 100% reliable - you've given her the cheaper test. You know the following things about the cheaper test:

1% of women who take the test do in fact have breast cancer.
Of the women who do have breast cancer, 80% will get a positive result from this test, 20% negative.
Of the women who do not have breast cancer, 9.6% will get a false positive result from this test, and 90.4% of them will get a negative result.

What do you think her probability of having cancer his, after getting a positive result from this test?

Don't worry about getting the answer wrong - literally 85% of doctors also get it wrong. What does your intuition tell you?

Replying to out-standing posts..

So.. regardless of the outcome of the tests, she either has or has not got cancer, so a 50/50 probability of having cancer.

..or have I been too pragmatic with my answer. :-k
The possibility of anything we can imagine existing is endless and infinite.. ~MagsJ

I haven't got the time to spend the time reading something that is telling me nothing, as I will never be able to get back that time, and I may need it for something important at some point in time.. Huh!? ~MagsJ

You’re suggestions and I just simply don’t mix.. like oil on water, or a very bad DJ ~MagsJ

Examine what is said, not him who speaks ~Arab proverb

aes Sanātana Dharma Pali: the eternal way ~it should not be rigid, but inclusive of the best of all knowledge for the sake of Ṛta.. which is endless.
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Re: For Magsj: Bayes Theorem and Why It's Relevant

Postby Flannel Jesus » Tue Aug 16, 2022 1:49 pm

Do you have a 50/50 chance of dying tomorrow? After all, you either will or you won't. 50/50 right?
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Re: For Magsj: Bayes Theorem and Why It's Relevant

Postby Flannel Jesus » Tue Aug 16, 2022 2:32 pm

The answer most people intuitively give is 80%. They read this and tend to discount the rest of the information very quickly:

"Of the women who do have breast cancer, 80% will get a positive result from this test, 20% negative."

80% seems like an intuitive number to pull out of there, but they're missing one very important detail:

People without Cancer outnumber people with cancer, drastically.

"1% of women who take the test do in fact have breast cancer.
Of the women who do have breast cancer, 80% will get a positive result from this test, 20% negative.
Of the women who do not have breast cancer, 9.6% will get a false positive result from this test, and 90.4% of them will get a negative result."

For every woman with breast cancer taking the test, there are 99 without. And even though most people without cancer get a negative result, the amount that get a positive result is still 9.6%, which still means that actually, you're expecting most people who get a positive result to not actually have cancer.

Think about it like if you were to have a group of 1000 people who represent the data set perfectly.

1% have cancer - that's 10 people. 80% of people with cancer get a positive result - that's 8 people with cancer and a positive result.

99% do not have cancer - that's 990 people. 9.6% of them get a positive result - that's about 95 people with no cancer, but with a positive result.

Which means, if you get a positive result, you're not 80% likely to have cancer - you're far more likely to not have cancer. More than 10 times more likely to not have cancer, in fact.

Bayes theorem is a formalization of this logic, essentially. It's a way that explicitly forces us to not throw away the useful information about what the likelihood of seeing this result is, in both cases, and the likelihood of both cases to begin with. All that information is relevant.
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Re: For Magsj: Bayes Theorem and Why It's Relevant

Postby Flannel Jesus » Tue Aug 16, 2022 2:36 pm

P(A|B)=P(B|A) * P(A) / P(B)
A, B = events
P(A|B) = probability of A given B is true
P(B|A) = probability of B given A is true
P(A), P(B) = the independent probabilities of A and B

That's the formalization of it, and when applied correctly, it forces you to consider every detail, so you avoid the pitfall that leads to the intuitive but incorrect conclusion of 80%
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Re: For Magsj: Bayes Theorem and Why It's Relevant

Postby MagsJ » Tue Aug 16, 2022 4:27 pm

_
1% do in fact have breast cancer.

So the probability of her having cancer are 1 in 100, so 0.01%
Last edited by MagsJ on Tue Aug 16, 2022 4:33 pm, edited 2 times in total.
The possibility of anything we can imagine existing is endless and infinite.. ~MagsJ

I haven't got the time to spend the time reading something that is telling me nothing, as I will never be able to get back that time, and I may need it for something important at some point in time.. Huh!? ~MagsJ

You’re suggestions and I just simply don’t mix.. like oil on water, or a very bad DJ ~MagsJ

Examine what is said, not him who speaks ~Arab proverb

aes Sanātana Dharma Pali: the eternal way ~it should not be rigid, but inclusive of the best of all knowledge for the sake of Ṛta.. which is endless.
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Re: For Magsj: Bayes Theorem and Why It's Relevant

Postby Flannel Jesus » Tue Aug 16, 2022 4:30 pm

Breast Cancer is not a joke magsj, you should feel very ashamed
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Re: For Magsj: Bayes Theorem and Why It's Relevant

Postby MagsJ » Tue Aug 16, 2022 4:36 pm

Flannel Jesus wrote:Breast Cancer is not a joke magsj, you should feel very ashamed

I was laughing at my not having instantly taken that stat into account, not at the 1% having cancer.

Please see my prior amended-post.
The possibility of anything we can imagine existing is endless and infinite.. ~MagsJ

I haven't got the time to spend the time reading something that is telling me nothing, as I will never be able to get back that time, and I may need it for something important at some point in time.. Huh!? ~MagsJ

You’re suggestions and I just simply don’t mix.. like oil on water, or a very bad DJ ~MagsJ

Examine what is said, not him who speaks ~Arab proverb

aes Sanātana Dharma Pali: the eternal way ~it should not be rigid, but inclusive of the best of all knowledge for the sake of Ṛta.. which is endless.
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Re: For Magsj: Bayes Theorem and Why It's Relevant

Postby Flannel Jesus » Tue Aug 16, 2022 4:40 pm

MagsJ wrote:_
1% do in fact have breast cancer.

So the probability of her having cancer are 1 in 100, so 0.01%

That's the probability before the test - the question is, what's the probability after the test? After the test comes back positive?
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Re: For Magsj: Bayes Theorem and Why It's Relevant

Postby Ichthus77 » Fri Aug 19, 2022 3:17 am

FJ: With or without a profit-driven health care industry?
Fall semester ends 12/16/22. Apologies if I do not reply immediately.

“In choosing myself, I choose the other.”
- A marriage of Sartre & Levinas

“ Gloria Dei est vivens homo. “
Trans.: The glory of God is man fully alive.
- Irenaeus

Excuse #2 why I’m not dating: I want to be able to say I haven’t shaved in a decade.

Excuse #1 “I wouldn’t want to join any club that would have me as a member.” - Groucho Marx

Excuse #3: I wouldn’t want to get too attached right before Mutually Assured Destruction.

Follow me for more excuses.
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Re: For Magsj: Bayes Theorem and Why It's Relevant

Postby Flannel Jesus » Fri Aug 19, 2022 8:24 am

Everybody wants to make everything into a trick question lmao
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Re: For Magsj: Bayes Theorem and Why It's Relevant

Postby Sculptor » Fri Aug 19, 2022 10:23 am

Flannel Jesus wrote:Everybody wants to make everything into a trick question lmao


Oh yeah???
What exactly do you mean by that??
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Re: For Magsj: Bayes Theorem and Why It's Relevant

Postby Flannel Jesus » Fri Aug 19, 2022 10:27 am

Hmmm...
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Re: For Magsj: Bayes Theorem and Why It's Relevant

Postby MagsJ » Fri Aug 19, 2022 10:37 am

_
Hahaha! what does Sculptor mean by that? :-s

I’ll try do the math, and get back to you as imminently as is possible.. I’m finding this quite interesting an endeavour to undertake. :-k
The possibility of anything we can imagine existing is endless and infinite.. ~MagsJ

I haven't got the time to spend the time reading something that is telling me nothing, as I will never be able to get back that time, and I may need it for something important at some point in time.. Huh!? ~MagsJ

You’re suggestions and I just simply don’t mix.. like oil on water, or a very bad DJ ~MagsJ

Examine what is said, not him who speaks ~Arab proverb

aes Sanātana Dharma Pali: the eternal way ~it should not be rigid, but inclusive of the best of all knowledge for the sake of Ṛta.. which is endless.
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