All Questions
Tagged with conditional-independence bayesian
7
questions
0
votes
1
answer
153
views
Dependence through an unknown parameter?
Consider an urn from which we sample with replacement. Let $\pi$ represent the proportion of the urn's balls that are black, with the remainder being white.
From a frequentist perspective, each ...
0
votes
0
answers
9
views
Bayesian network extracting further conditional independence statements then just from d-separation theorem
Given a Bayesian network $(p,\mathcal{G})$, where $p$ is our joint distribution, and $\mathcal{G}$ is a DAG.
Then by the d-separation theorem we can deduce conditional independence statements, in ...
0
votes
0
answers
31
views
Bayes Rule with conditional independence of two tests based on a common blood sample
I have the following scenario of Bayes updating with which I struggle quite a bit.
Imagine we are interested in the probability that a given person has a disease $D$. We perform two different tests $...
1
vote
1
answer
86
views
How to show mathematically whether the following conditional relationships hold?
In the following Bayesian network, the variables $ x_{i} $ are mutually independent (let's assume that these are the positions of $N$ boats). The variables $ y_{i,j} $ are distance measurements ...
6
votes
1
answer
663
views
Are two coin flips conditionally independent if we know that the coin is biased towards heads?
Suppose Alice (A) and Bob (B) each flip the same, potentially-biased coin. Then, P(A=H) < P(A=H | B=H), because Bob's flip increases our suspicion that the coin is biased towards heads.
Now ...
0
votes
0
answers
833
views
Naive bayes example by hand
Given the following data
...
1
vote
1
answer
187
views
Assuming n variables are conditionally independent given y, how do I compute p(y | x_1,...,x_n)?
Referencing this question, I know that if $x_1$ and $x_2$ are conditionally independent given $y$ (big assumption), then
$$P(y | x_1,x_2) = \frac{P(x_1,x_2 | y)P(y)}{P(x_2 | x_1)P(x_1)}$$
$$ = \frac{...