The approach and interpretation of probability associated with Bayes' theorem; usually used as opposed to the frequentist approach. It can be seen as an extension of logic that enables reasoning with propositions whose truth or falsity is uncertain. A Bayesian probabilist starts with some prior probability, and evaluates the evidence in favour of a hypothesis by combining the prior with the likelihood function of the observed data.
Questions tagged [bayesian]
2030 questions
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Bayesian probability of drawing balls
I have a question like "Given that there are 4 balls in a bag with unknown colour, suppose you draw the black ball for the first time. What is the probability that you draw the black ball the next three times?" Could anyone provide some suggestion…
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Problem with some Bayesian posterior pdf functions.
I've been given a problem and I'm not entirely sure how to approach it, I'm aware of the basics like $Posterior ∝ Likelihood × Prior$ etc. but I'm not sure what steps to take here to solve the below problem.
Any help would be greatly…
MathewG
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Probability of choosing M out of N Groups given that all A elements are inside M
Assuming I have A number of individuals who are randomly distributed into N number of groups.
What is the probability of finding A (or any number a <= A) by picking M number of groups within N?
I figured that there are P(M, A) ways that the…
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Bayesian: Calculate posterior when the prior is a mixture of two beta distributions
Suppose you have a prior that is a mixture of two beta distributions, like so: prior = (0.5)dbeta(a1,b1) + (1-0.5)dbeta(a2,b2). Furthermore, suppose you just recently ran a binomial experiment with 'x' successes out of 'n' trials and want to…
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Communication Theory - Maximum A Posteriori (MAP) Principle
I'm taking a communication theory course and I have some confusion regarding the maximum a posteriori rule.
In my notes it says that,
Consider a communication system where the transmit symbols are x from a choice of J possible symbols. The received…
AlfroJang80
- 253
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Looking for conjugate priors for a Binomial likelihood
The likelihood function is a Binomial one -- say $k$ failures in $n$ trails given the probability of failure is $p$.
The $p$ is a function of two independent r.v. $x$ and $y$: $p=a-bx+cy$ where $a$, $b$ and $c$ are known constants in the range of…
weidade3721
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Which of the following factorization captures most accurately the assumptions described?
Suppose you want to use a Bayesian network to model your performance in an exam. Your performance on the exam will depend only on whether the exam is easy and whether you studied enough. In addition, how much time you devote to studying for this…
Cheryl
- 249
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KL divergence minimization
I have seen different derivations of KL divergence problems. Up to here, I understand everything:
Then in next step we get:
See:
But this just can not be true:
I am sure I am missing something, but I just can not understand it what.
additional…
filtertips
- 305
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Updated belief with Bayes' rule
Let $\{x_0,x_1\}$ be to states. Suppose the reward is $1$ in state $x_1$, and in state $x_0$ it is $1$ with probability $r$ and $0$ with probability $1-r$, with $r\in(0,1)$.
Bob has a belief $p\in [0,1]$ over the states $x_0$ and $x_1$, i.e., $p$ is…
S. Pel
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Accept - Reject of Normal Distribution with prior Cauchy
If $X \sim N(\theta,1)$ with Cauchy as robust prior
$$\pi(\theta) = \frac{1}{\pi(1+\theta^2)} \qquad -\infty < \theta < \infty$$
how to do the rejection sampler in R, and use it to generate 10, 000 samples from the posterior distribution. with using…
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ordered data - probability distribution
I have n items ranked by k experts. I would like to aggregate the ranks using a Bayesian model. However, I do not know if there is a way to model the ranks.
P.S.: You can assume that we have a feature vector for each item, although I prefer that…
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Why are $p(y)$ called "prior frequencies for classes"?
Why are $p(y)$ called "prior frequencies for classes"?
Since they apply on $y$, not $x$. But since the prediction is made $x \rightarrow y$, then $y$ should be posterior, right?
Particularly, this is in the context of Naive Bayes Classifier.
Or do…
mavavilj
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Bayes estimation problem
Here is the problem description.
Given the following generative model, p(x|y)~N(y,1), where x is the observation and y is the state/category.
Given that the a-priori distribution of y is y ~ N(z, 1/s) (where s and z are
parameters).Calculate the MAP…
Kai Xie
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Different versions of Bayes Theorem
Given this formula:
$$P(A|B)=\frac{P(B|A)P(A)}{P(B)}=\frac{P(A∧B)}{P(A∧B)+P(¬A∧B)}$$
The second part is the Bayesian formula, the third part is what I thought the Bayesian formula must be based on my own reasoning.
Question:
Is this equality true?…
GambitSquared
- 3,662
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understand Bayesian probability fastest
I am looking for a good book to learn at least joint probability Bayes rules. I have a bit of experience with probabilities. I have got a course last semester in stochastic process. Could anyone be able to refer to me a good book for understand…
J.Doe
- 13