# Tagged Questions

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 ...

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### A confusing excersice about Bayes' rule

The following is from a textbook one bayesian stats. that I can't understand some deduction. It is relevant about multiple parameters to be estimated. The jth observation in the ith group is denoted ...
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### Bayes Theorem with joint probability evidence?

If I am trying to compute the probability $P(Z\mid(A,B))$ using Bayes' Theorem, how would I expand the right-hand side, particularly the evidence $P(A,B)$ in the denominator?
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### In Bayesian Statistic how do you usually find out what is the distribution of the unknown?

To estimate the posterior we have $$p(\theta|x) = \frac{p(\theta)*p(x|\theta)}{\sum p(\theta ')*p(x|\theta ')}$$ $x$ is usually the experimentally sampled data, and $\theta$ is the model, but both ...
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### I am confused about Bayes' rule in MCMC

Bayes' rule appears to bevery simple at first sight, but when studied deeply I find it is difficult and confusing, especially in MCMC applications when multiple parameters need to be estimated. For ...
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### combining conditional probabilities

I've come across a physics paper in which pdf $$p(a|b)$$ is desired, but only $$p(a|c)\\ p(c|b)$$ are known. It is claimed that $$p(a|b)=\int p(a|c)p(c|b) dc.$$ Is this correct wlog? I can't ...
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### Coin toss - probability of a tail known that one is heads

A friend of mine tossed a fair coin twice. Suppose I ask him whether he got a head in the two tosses, and he says yes. What is the probability that one toss is tail? Now suppose instead that I happen ...
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### conditional probability of joints

I have been staring at a bayesian net for an hour and can't understand why this is correct to write: $$P(A|B,E)\cdot P(W|A) = P(W,A|B,E)$$ Note that the joint probability of $P(A,B,E,W,R)$ can be ...
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### Probability question: given $P(A|B)$ and $P(B)$ how do I find $P(A)$?

I have a probability distribution for some quantity $A$ given a fixed $B$, i.e. $P(A|B)$. I also have a prior distribution $P(B)$ for $B$. I'm trying to find the distribution $P(A)$. I had thought ...
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### Is there an introduction to probability and statistics that balances frequentist and bayesian views?

Perhaps, roughly, I might be described as advanced undergraduate regarding mathematics. However, I have not learned statistics and have only learned elementary probability. Does there exist a book or ...
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### Bayes rule with multiple conditions

I am wondering how I would apply Bayes rule to expand an expression with multiple variables on either side of the conditioning bar. In another forum post, for example, I read that you could expand ...
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### Bayes, two tests in a row

I came up with a standard Bayesian example as to point out my confusion. There is an epidemic. A person has a probability $\frac{1}{100}$ to have the disease. The authorities decide to test the ...
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### Kolmogorov's paper defining Bayesian sufficiency

I'm looking for a translation to either English, French or German of Kolmogorov's Russian paper Kolmogorov, A. (1942). Sur l’estimation statistique des paramètres de la loi de Gauss. Bull. Acad. Sci. ...
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### Extended Bayes' theorem: p(A | B, C, D)

I'm having some difficulty understanding Bayes' theorem with multiple events. I'm trying to put together a Bayesian network. I have four independent probabilities but I have found that A, B and C can ...
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### question related to Bayes' rule and Bays' risk.

Let $X_1, X_2, X_3, \ldots, X_n$ be a random sample for $N(e,1)$. Let the prior p.d.f. of $e$ be $N(0,\sigma^2)$ under the square error loss function $L(e,d)={(d-e)}^2$. Find the Bayes' decision rule ...
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### Separate expression $c(x + y)^2 e^{yz}$

Considering the following expression, with $x, y, z, c \in \mathbb{R}$, is such expression separable into $f(x, y, z) = g(x, z)h(y, z)$? $c(x + y)^2 e^{yz}$ If not, why isn't it separable? Note: ...
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### If $P(B\text{ }|\text{ }A)=1-\epsilon$ and $P(C\text{ }|\text{ }B)=1$ then $P(C\text{ }|\text{ }A)\geq 1-\epsilon$ [duplicate]

If $$1=P(C\text{ }|\text{ }B)=\frac{P(C\cap B)}{P(B)}$$ then we know that $P(C\cap B)=P(B)$. If $P(B\text{ }|\text{ }A)=1-\epsilon$ for $\epsilon\geq 0$ then P(A)=\frac{P(B\cap ...
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### Building Bayesian Networks, Causality and Cyclic Reasoning

I am studying Bayesian Statistics and I am trying to get a good understanding on Bayesian Networks, which seems to be vital in order to make something useful in Machine Learning. Most of the texts I ...