This link has been bookmarked by 116 people . It was first bookmarked on 02 Mar 2006, by Hugh Bristic.
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Joe Rowe"The probability that a woman with a positive mammography has breast cancer" is not at all the same thing as "the probability that a woman with breast cancer has a positive mammography"; they are as unlike as apples and cheese.
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Joe Rowe"The probability that a woman with a positive mammography has breast cancer" is not at all the same thing as "the probability that a woman with breast cancer has a positive mammography"; they are as unlike as apples and cheese.
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These two extreme examples help demonstrate that the mammography result
doesn't replace your old
information about the patient's chance of having cancer; the
mammography slides the
estimated probability in
the direction of the result. A positive result slides the
original
probability upward; a negative result slides the probability
downward. -
Most people encountering problems of this type for the first time carry
out the mental operation of replacing
the original 1% probability with the 80% probability that a woman with
cancer gets a positive mammography. It may seem like a good idea,
but it just doesn't work. - 28 more annotations...
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Jonathan Broadintuitive indeed...
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François ParmentierHere you will find an attempt to offer an intuitive explanation of Bayesian reasoning
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People do not employ Bayesian reasoning intuitively, find it very difficult to
learn Bayesian reasoning when tutored, and rapidly forget Bayesian methods once
the tutoring is over -
Bayesian problems in your dreams.
- 2 more annotations...
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Even if mammography
in this world detects
breast cancer in 8 out of 10 cases, while returning a false positive on
a woman without breast cancer in only 1 out of 10 cases, there will
still be a hundred thousand false positives for every real case of
cancer detected.
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Olifante *"science itself is a special case of Bayes' Theorem; experimental evidence is Bayesian evidence. [...] Karl Popper's falsificationism [...] is the old philosophy that the Bayesian revolution is currently dethroning."
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Bayes' Theorem
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Your friends and colleagues are talking about something called "Bayes' Theorem" or "Bayes' Rule", or something called Bayesian reasoning. They sound really enthusiastic about it, too, so you google and find a webpage about Bayes' Theorem and...
It's this equation. That's all. Just one equation. The page you found gives a definition of it, but it doesn't say what it is, or why it's useful, or why your friends would be interested in it. It looks like this random statistics thing.
So you came here. Maybe you don't understand what the equation says. Maybe you understand it in theory, but every time you try to apply it in practice you get mixed up trying to remember the difference between p(a|x) and p(x|a), and whether p(a)*p(x|a) belongs in the numerator or the denominator. Maybe you see the theorem, and you understand the theorem, and you can use the theorem, but you can't understand why your friends and/or research colleagues seem to think it's the secret of the universe. Maybe your friends are all wearing Bayes' Theorem T-shirts, and you're feeling left out. Maybe you're a girl looking for a boyfriend, but the boy you're interested in refuses to date anyone who "isn't Bayesian". What matters is that Bayes is cool, and if you don't know Bayes, you aren't cool.
Why does a mathematical concept generate this strange enthusiasm in its students? What is the so-called Bayesian Revolution now sweeping through the sciences, which claims to subsume even the experimental method itself as a special case? What is the secret that the adherents of Bayes know? What is the light that they have seen?
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Bayes' Theorem for the curious and bewildered; an excruciatingly gentle introduction.
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Your friends and colleagues are talking about something called "Bayes' Theorem" or "Bayes' Rule", or something called Bayesian reasoning. They sound really enthusiastic about it, too, so you google and find a webpage about Bayes' Theorem and...
It's this equation. That's all. Just one equation. The page you found gives a definition of it, but it doesn't say what it is, or why it's useful, or why your friends would be interested in it. It looks like this random statistics thing. -
Your friends and colleagues are talking about something called "Bayes' Theorem" or "Bayes' Rule", or something called Bayesian reasoning. They sound really enthusiastic about it, too, so you google and find a webpage about Bayes' Theorem and...
It's this equation. That's all. Just one equation. The page you found gives a definition of it, but it doesn't say what it is, or why it's useful, or why your friends would be interested in it. It looks like this random statistics thing. - 1 more annotations...
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An Intuitive Explanation of Bayesian Reasoning
Bayes' Theorem
for the curious and bewildered;
an excruciatingly gentle introduction.
By Eliezer Yudkowsky
Your friends and colleagues are talking about something called "Bayes' Theorem" or "Bayes' Rule", or something called Bayesian reasoning. They sound really enthusiastic about it, too, so you google and find a webpage about Bayes' Theorem and... -
An Intuitive Explanation of Bayesian Reasoning
Bayes' Theorem
for the curious and bewildered;
an excruciatingly gentle introduction.
By Eliezer Yudkowsky
Your friends and colleagues are talking about something called "Bayes' Theorem" or "Bayes' Rule", or something called Bayesian reasoning. They sound really enthusiastic about it, too, so you google and find a webpage about Bayes' Theorem and... - 1 more annotations...
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Ben ButtigiegFacinating article about Bayesian Reasoning
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other." In one sense, this is correct - any correlation, no matter how weak, is fair prey for Bayes' Theorem; but Bayes' Theorem distinguishes between weak and strong evidence. That is, Bayes' Theorem not only tells us what is and isn't evidence, it also describes the strength of evidence. Bayes' Theorem not only tells us when to revise our probabilities, but how much to revise our probabilities. A correlation between hope and biological warfare may exist, but it's a lot weaker than the speaker wants it to be; he is revising his probabilities much too far.
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Matt KoidinGood read for some time...
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Or so they claim. Here you will find an attempt to offer an intuitive explanation of Bayesian reasoning - an excruciatingly gentle introduction that invokes all the human ways of grasping numbers, from natural frequencies to spatial visualization. The intent is to convey, not abstract rules for manipulating numbers, but what the numbers mean, and why the rules are what they are (and cannot possibly be anything else). When you are finished reading this page, you will see Bayesian problems in your dreams.
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Your friends and colleagues are talking about something called "Bayes' Theorem" or "Bayes' Rule", or something called Bayesian reasoning. They sound really enthusiastic about it, too, so you google and find a webpage about Bayes' Theorem and...
It's this equation. That's all. Just one equation. The page you found gives a definition of it, but it doesn't say what it is, or why it's useful, or why your friends would be interested in it. It looks like this random statistics thing.
So you came here. Maybe you don't understand what the equation says. Maybe you understand it in theory, but every time you try to apply it in practice you get mixed up trying to remember the difference between p(a|x) and p(x|a), and whether p(a)*p(x|a) belongs in the numerator or the denominator. Maybe you see the theorem, and you understand the theorem, and you can use the theorem, but you can't understand why your friends and/or research colleagues seem to think it's the secret of the universe. Maybe your friends are all wearing Bayes' Theorem T-shirts, and you're feeling left out. Maybe you're a girl looking for a boyfriend, but the boy you're interested in refuses to date anyone who "isn't Bayesian". What matters is that Bayes is cool, and if you don't know Bayes, you aren't cool. -
Your friends and colleagues are talking about something called "Bayes' Theorem" or "Bayes' Rule", or something called Bayesian reasoning. They sound really enthusiastic about it, too, so you google and find a webpage about Bayes' Theorem and...
It's this equation. That's all. Just one equation. The page you found gives a definition of it, but it doesn't say what it is, or why it's useful, or why your friends would be interested in it. It looks like this random statistics thing.
So you came here. Maybe you don't understand what the equation says. Maybe you understand it in theory, but every time you try to apply it in practice you get mixed up trying to remember the difference between p(a|x) and p(x|a), and whether p(a)*p(x|a) belongs in the numerator or the denominator. Maybe you see the theorem, and you understand the theorem, and you can use the theorem, but you can't understand why your friends and/or research colleagues seem to think it's the secret of the universe. Maybe your friends are all wearing Bayes' Theorem T-shirts, and you're feeling left out. Maybe you're a girl looking for a boyfriend, but the boy you're interested in refuses to date anyone who "isn't Bayesian". What matters is that Bayes is cool, and if you don't know Bayes, you aren't cool.
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p(A|X) = p(X|A)*p(A)
p(X|A)*p(A) p(X|~A)*p(~A)
Why wait so long to introduce Bayes' Theorem, instead of just showing it at the beginning? Well... because I've tried that before; and what happens, in my experience, is that people get all tangled up in trying to apply Bayes' Theorem as a set of poorly grounded mental rules; instead of the Theorem helping, it becomes one more thing to juggle mentally, so that in addition to trying to remember how many women with breast cancer have positive mammographies, the reader is also trying to remember whether it's p(X|A) in the numerator or p(A|X), and whether a positive mammography result corresponds to A or X, and which side of p(X|A) is the implication, and what the terms are in the denominator, and so on. In this excruciatingly gentle introduction, I tried to show all the workings of Bayesian reasoning without ever introducing the explicit Theorem as something extra to memorize, hopefully reducing the number of factors the reader needed to mentally juggle.
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Here you will find an attempt to offer an intuitive explanation of Bayesian reasoning - an excruciatingly gentle introduction that invokes all the human ways of grasping numbers, from natural frequencies to spatial visualization. The intent is to convey, not abstract rules for manipulating numbers, but what the numbers mean, and why the rules are what they are (and cannot possibly be anything else). When you are finished reading this page, you will see Bayesian problems in your dreams.
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