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Questions tagged [bayes-theorem]

For questions related to Bayes' theorem, a result about conditional probabilities.

Bayes' theorem relates probabilities of events with conditional probabilities. In its most common form, the result states that if $A$ and $B$ are events, then

$$P(A | B) = \frac{P(B|A) P(A)}{P(B)}$$

where $P(A | B)$ is the conditional probability of $B$ given $A$.

Interpretations of this statement vary according to the Bayesian interpretation, and the Frequentist interpretation.

Reference: Bayes' Theorem.

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Bayes's theorem from Tversky and Kahneman in Michael Lewis's The Undoing Project

Michael Lewis's book "The Undoing Project" is concerned with the (mathematical) psychologists Daniel Kahneman and Amos Tversky. (Kahneman won the 2002 Nobel Prize; Tversky died in 1996.) On page 157, this question is quoted: The mean IQ of the…
Frank Wang
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How to start with Bayes theorem

I'm just learning about Bayes, I don't have any Math background at all, so this is really a newbie question. I know there are lots of questions about Bayes here already but most involve some kind of added complexity on top of the basic formula. So…
Kokodoko
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Probability of both kids being a girl given one is a girl

So I found this teaser: A mom has two kids. Given one of them is a girl, what's the probability that both are girls? The answer is 1/3. Which I have reasoned with the following. There are four possible outcomes for two kids, BB, BG, GB, GG. Given…
sedavidw
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Bayes theorem P(A) for second step

Here is the problem. Alice went to doctor and doctor said test will produce 99% true result for ill people and 99% true negative for non-ill people. For this particular illness there is 1 per 1000 who get ill. So I implemented this in bayes theorem…
filtertips
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If the event has occured in the past, does it have probability of 1?

The problem is like that: "John wakes up with a sore throat. Use Bayes’ rule to infer the posterior probability distribution for what John’s ailment is. Show your final result to three decimal places" I am not given $P(\text{sore throat})$, does it…
Augustas
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Q. Bayes' rule problem

Imagine I have two events $A$ and $B$. On a day only one event can occur and $P(A) = 0.05$ and $P(B) = 0.95$. Also, let there be another event $C$ that occurs where, $P(C | A) = 0.8$ and $P(C | B) = 0.1$. How do I calculate the probability of $C$…
Kobe00992
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Probability using Bayes Theorum

Here's a problem which me and a friend had an argument over the answer. Could someone please resolve the dispute People are first subjected to test_1, if the test_1 is positive then person is taken for test_2. Test_2 will reveal whether the person…
mantd
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Bayes' theorem and partition of S

Use Bayes' theorem or a tree diagram to calculate the indicated probability. Round your answer to four decimal places. Y1, Y2, Y3 form a partition of S. P(X | Y1) = .8, P(X | Y2) = .1, P(X | Y3) = .9, P(Y1) = .1, P(Y2) = .4. Find P(Y1 | X). P(Y1 |…
user344249
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How to do Bayes' theorem?

Use Bayes' theorem or a tree diagram to calculate the indicated probability. Round your answer to four decimal places. P(A | B) = .9, P(B) = .6, P(A | B') = .8. Find P(B | A). We don't have an example like this in class so I was wondering if someone…
user344249
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Intuition behind a particular formulation of Bayes's Theorem : $\dfrac{P(A\mid B)}{P(A)} = \dfrac{P(B\mid A)}{P(B)}$?

Bayes's theorem states $P(A\mid B) = \dfrac{P(B\mid A)\cdot P(A)}{P(B)}$. The intuition behind this is simple: if $B$ is true, then the probability that $A$ is true is the number of cases where $A$ is true out of all cases where $B$ is true. Now,…
Eric Brooks
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interpretting prior and posterior

I am bit puzzled on how we can interpret the posterior. Assume a coin which is 0.1 probable to be unfair. So our prior probability on the coin being unfair is 0.1, and being fair is 0.9. Also by unfair I mean, the probability of head is 2/3 instead…
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Bayes' Theorem and Probability

Suppose that you are diagnosed with microscopic hematuria (blood in the urine that is only visible under a microscope). This symptom occurs in 10 percent of all people and 100 percent of people with kidney cancer. You would like to know the…
user137387
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Order of variables in Bayes network total probabily expansion?

I've asked this question on Udacity, no response. It goes like this. There's a network with A at the root, and three X variables dependent on A. The probability of each given A is equal, and they are conditionally independent. The problem is to get…
Chara
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Why is the numerator of Baye's Theorem $P(A\cap B)$ instead of $P(A|B)$?

For example, say I have am holding an object; $O$ is the event that the object is an orange, and $R$ is the event that the object is round. $P(O|R) = \frac{P(R|O)}{P(R)}$ This is obviously incorrect, but it reads to me like: "the probability that…
Each One Chew
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Bayes' Rule for events exercise: what is the probability that vampires exist?

It's an exercise from the online book Bayes Rules! An Introduction to Bayesian Modeling with R. Thus the book has no chapter with the right answers and so far I've not found a designated place to discuss its exercises, let's do the discussion…
Raibek
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