# Questions tagged [jeffreys-prior]

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10 questions
1k views

### Example for a prior, that unlike Jeffreys, leads to a posterior that is not invariant

I am reposting an "answer" to a question that I had given some two weeks ago here: Why is the Jeffreys prior useful? It really was a question (and I did not have the right to post comments at the time,...
2k 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 ...
313 views

### Using variance from a Jeffreys prior in a Prevalence meta-analysis

I am doing a meta-analysis on a group of studies, where the observation is a rate (no. of successes / no of trials). Some of the studies have small sample sizes (n<10) and/or did not observe any ...
875 views

### What is the relation behind Jeffreys Priors and a variance stabilizing transformation?

I was reading about the Jeffreys prior on wikipedia: Jeffreys Prior and saw that after each example, it describes how a variance-stabilizing transformation turns the Jeffreys prior into a uniform ...
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### Jeffreys Prior for normal distribution with unknown mean and variance

I am reading up on prior distributions and I calculated Jeffreys prior for a sample of normally distributed random variables with unknown mean and unknown variance. According to my calculations, the ...
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### What reparametrization of vector parameters makes the Jeffreys prior correspond to the uniform prior?

What reparametrization of vector of parameters $\theta$ makes the Jeffreys prior $$\sqrt{\det I(\theta)}$$ correspond to the uniform prior? A change of parametrization from $\theta$ to $\eta$ changes ...
120 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 ...
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### 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 ...
139 views

### How to choose a importance density for Jeffreys prior?

I want to draw Bayesian inference via importance sampling and I do not come up with a good idea of an importance density for $$p(\sigma)\sim\frac{1}{\sigma}.$$ Is there a way to sample from this ...
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### 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, ...