Tagged Questions
9
votes
5answers
1k views
Bayes Theorem Example in Nate Silver's The Signal and the Noise
In his book The Signal and the Noise, Nate Silver presents this example application of Bayes's Theorem on pp. 247-248:
Consider a somber example: the September 11 attacks. Most of us would
have ...
4
votes
1answer
82 views
Does Bayesian probability have a different interpretation of a random variable?
Bayesian probability interprets the meaning of the probability of a random variable as some degree of belief. But does this result in any difference in the interpretation of a random variable itself?
...
4
votes
0answers
329 views
Trying to understand the basics of bayesian inference
This paper gives a somewhat gentle introduction to Bayesian inference: http://www.miketipping.com/papers/met-mlbayes.pdf
I got to section 2.3 without much problems but got stuck in understanding that ...
3
votes
1answer
36 views
Bayesian formula for weather exercise
If it is nice weather on one day, the probability that it is going to be nice again the next is $13/15$.
If it is raining on one day, the prob. that it is going to be raining again the next day is ...
2
votes
6answers
211 views
What is the probability of the box?
Your box of cereal may be a contest winner! It's rattling, which 100% of winning boxes do. Of course 1% of all boxes rattle and only one box in a million is a winner. What is the probability that your ...
2
votes
1answer
51 views
What is the probability of two or more from n events occuring?
A number of independent events, say $A$, $B$, $\ldots\,$, $E$, can happen with associated probabilities $P(A)$, $P(B)$, $\ldots$
For each event that happens I have to pay £10. The likelihood I have ...
2
votes
1answer
118 views
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 ...
2
votes
1answer
62 views
On Finding Means of Distributions
If I have a distribution which depends only on one variable, I usually find the mean by:
(Continuous Case)
$$\mu=\displaystyle \int xf_X(x).dx$$
What happens in the following cases:
Conditional ...
2
votes
1answer
66 views
Conditional Probability Question
There are three events, $A$, $B$ and $D$. I know that $P(D)=0.2$, $P(A)=0.34$ and $P(B)=0.43$. I have calculated that $P(D\mid A)=0.5294$ and $P(D\mid B)=0.44186$. Now I need to calculate $P(D\mid ...
2
votes
2answers
231 views
Finding Probability of P(S|W) at Bayesian Network of Rain Problem
I am studying Bayesian Networks. Given that variables:
$W$: Wet grass
$R$: Rain
$S$: Sprinkler
I know the probabilities of:
$P(C)$
$P(S | C)$
$P(S | !C)$
$P(R | C)$
$P(R | !C)$
$P(W | R,S)$
$P(W | ...
2
votes
1answer
111 views
A confusing excersice about Bayes' rule
The following is from a textbook one bayesian stats. that I can't understand some deduction. It is relevant about multiple parameters to be estimated.
The jth observation in the ith group is denoted ...
2
votes
1answer
38 views
What is the meaning of “mean-field”?
In lots of Bayesian papers, people use variational approximation. In lots of them they call it "mean-field variational approximation". Does anyone know what is the meaning of mean-field in this ...
2
votes
0answers
47 views
Gaussian Bayesian filtering with bound observation ($b_1<x<b_2$)
Suppose we have a Normal r.v
$$ x \sim \mathcal{N}(\mu, \sigma^2) $$
and a Normal prior of $\mu$
$$ \mu \sim \mathcal{N}(\theta, \delta^2) $$
I know how to do the Bayesian update with a ...
2
votes
3answers
31 views
A bayesian way of calculating the probability $\text{Pr}(\theta \in (\theta_1, \theta_2) | y )$
I'm confused by a bayesian way of calculating the probability $\text{Pr}(\theta \in (\theta_1, \theta_2) | y )$, where $\theta$ is assumed to have a (prior) uniform distribution on $[0,1]$, and the ...
2
votes
1answer
52 views
Questions on Bayesian analysis of an opinion poll (an example in a book)
I'm sorry in advance for rather long questions. This is an example in "Bayesian logical data analysis for physical sciences" by P. C. Gregory and I have some questions about the example.
In a poll ...
