All Questions
Tagged with prior jeffreys-prior
30
questions
3
votes
1
answer
691
views
Jeffreys prior of a multivariate Gaussian
I have found two different expressions for the Jeffreys prior of a multivariate Gaussian. Eq. (3) in this article states that $$p(\mu,\Sigma) \propto \det(\Sigma)^{-(d+2)/2}$$
However in page 73 of ...
- 956
1
vote
1
answer
118
views
Which form of Jeffrey's prior can be used for a three-parameter distribution?
Let X be a random variable which follows a distribution, say S with parameters a, b and c. Knowing that or Assuming that a, b and c are independent of one another, which one is reasonable to do?
a) Is ...
- 362
1
vote
1
answer
107
views
Is there any strong argument about objective/non-informative improper prior?
Decades ago improper objective priors - e.g. $\pi(\sigma) \propto \sigma^{-1}, \sigma > 0,$ for a scale parameter - were considered problematic because some authors thought they were leading to the ...
- 51
4
votes
2
answers
1k
views
Informative priors for standard deviation (or variance)
Suppose I want to perform Bayesian estimation of the mean $\mu$ and standard deviation $\sigma$ of a Gaussian distribution. Is there a standard way to specify an informative prior over $\sigma$, ...
- 350
0
votes
0
answers
18
views
In what noninformative priors turn out to be informative? [duplicate]
When searching about noninformative priors on internet, one can read here and there that those priors in fact turn out to be informative. However, I did not yet read a real argument about that.
So my ...
- 1
1
vote
0
answers
441
views
Reference prior of normal distribution with unknow mean and variance
Problem:
Assume that $X|\theta \sim N(\theta, \sigma^2)$ for unknow $\theta$, and unknown $\sigma$.
a. Find the reference priors of $(\theta, \sigma)$, when $\sigma$ is of interest.
b. Find the ...
- 327
1
vote
0
answers
295
views
Postetior from Jeffrey prior of Normal distribtion
Context
I am given a sample from normal distribution $v_i \sim N(\gamma \cdot u_i, \sigma^2)$, $i =1,..., n$.
I need to obtain the posterior distribution using Jeffreys prior for $\gamma$.
My solution
...
- 261
0
votes
0
answers
643
views
Posterior Distribution of a Normal Sample using Jeffreys Prior with a Known Parameter
Suppose I have a sample of $x_1, x_2, ... x_n$, where $X \sim N(\mu, \sigma^2)$, for some known $\sigma^2$, and that $\mu$ is defined only in $\mu \in [0, b]$, for some finite constant $b$.
It then ...
- 83
2
votes
1
answer
877
views
Calculating Jeffreys Prior for geometric distribution
This question is already answered here, but I would like to know why it is worked out the way it is
My lecture notes state the following:
I am also given the following problem :
Now, what I ...
- 123
0
votes
1
answer
69
views
Are there situations where improper priors can be avoided via a prior on a subset of the real line and a transformation?
There are many situations where improper priors are "permissable" (Berger, 2009). In many cases, these improper priors are improper because they are "flat" on the real line. A well known example is ...
- 53
6
votes
1
answer
8k
views
Understanding definition of informative and uninformative prior distribution
When using the "non-informative" prior $\pi(\mu,\sigma)\propto\frac{1}{\sigma^2}$ where $\pi(\mu)\propto1$ and $\pi(\sigma^2)\propto\frac{1}{\sigma^2}$
Where is the no information for the ...
- 151
4
votes
1
answer
212
views
Objective Bayesianism: Jeffreys priors vs reference priors vs principle of transformation groups
According to this answer,
José Bernardo has produced an original theory of reference priors where he chooses the prior in order to maximise the information brought by the data by maximising the ...
- 993
3
votes
0
answers
103
views
What is the limit of this expression?
If $\det(\Lambda_0) \to 0$, what does
$$
\exp\left(-\frac{1}{2}\text{trace}\left(\Lambda_0 \Sigma^{-1}\right)\right)\det\left(\Lambda_0\right)^{-1/2}
$$
approach?
I was trying to answer the ...
- 21.2k
4
votes
2
answers
540
views
Obtaining Jeffreys prior by taking the limit of a particular prior density on $(\mu, \Sigma)$
Text: Bayesian Data Analysis 3E by Gelman, section 3.6
Let $y | \mu, \Sigma \sim \text{MVN}(\mu, \Sigma),$ where
$\mu$ is a column vector of length $d$
$\Sigma$ is a $d \times d$ symmetric, ...
- 665
11
votes
1
answer
5k
views
Why is uniform prior on log(x) equal to 1/x prior on x?
I'm trying to understand Jeffreys prior. One application is for 'scale' variables like the standard deviation $\sigma$ (or its square, the variance $\sigma^2$) of Gaussian distributions. It is often ...
- 263