Tagged Questions
0
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0answers
46 views
Estimating the radius of a circle
I have a circle iwth radius $r$. I want to test the hypothesis that $r \leq 2$ vs. $r >2$ based on the posterior of $r$. $r$ follows the prior distribution: $f(r) = \frac{2}{r^{2}}$, $ r >0.5$. ...
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42 views
Probability distribution for a digit of a number
If someone choose a digit $\alpha$ and a digit $\beta$ independently. Each one can be in $0,1, ...,9$. So $\mu = \alpha \beta$ (e.g. if $\alpha = 5$ and $\beta = 3$ then $\mu =53$). And I observe a ...
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0answers
20 views
Equivalence of Bayes and Classical Sufficiency
According to [BLA], classical sufficiency implies Bayes sufficiency and, in the dominated case - all $P_\theta$ absolutely continuous w.r.t. a single measure - Bayes sufficiency implies classical ...
1
vote
1answer
35 views
Bayesian learning
Imagine we assume there are two different types of coins:
Coin A: a fair coin, p(heads) = 0.5.
Coin B: biased to heads at p(heads)=0.7.
We then want to learn from samples which coin we are ...
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33 views
Hypothesis Testing Bayesian Way
I'm having trouble with the following problem:
Suppose a machine is composed of 2 components (1 and 2, independent from each other). Each component has a exponential failure probability distribution ...
1
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1answer
52 views
Two definitions of Bayes Sufficiency
"Bayes Sufficiency" is defined in two ways. Are they equivalent?
Setting
A statistical experiment $S$ is a triplet $\left(\left(\Theta,\mathcal{F}\right),\left(\Omega,\mathcal{A}\right),P\right)$, ...
4
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0answers
332 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 ...
