# Questions tagged [jeffreys-prior]

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### Why Is Jeffreys's Prior Used to Correct Biases?

I was reading this article on Logistic Regression for Rare Events. Over here, a modification ("Firth's Correction") to the classical likelihood function has been proposed in which a penalty ...
25 views

146 views

### Derive posterior density function with Jeffrey's prior for theta

I need a guide on how to derive the posterior distribution for $\theta$ and checking whether it is proper. I have been given that the likelihood function is $$L(\theta; x) = \theta \exp(−\theta x).$$ ...
1 vote
59 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 ...
72 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 ...
1 vote
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### Understanding the Jeffreys-Zellner-Siow (JZS) prior in Bayesian t-tests

I am currently working on a lecture on Bayesian hypothesis testing, following the paper by Rouder et al, 2009. On Page 231 they present the formula for the relevant Bayes factor based on the Jeffreys-...
1 vote
518 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 $\sigma$, ...
35 views

### Finding the posterior under Jeffreys prior

Let $U \sim \text{Unif}(0,1)$, $\alpha$ the rate parameter of interest and $a>0$ a fixed known constant, define $$X = a U^{-1/\alpha}$$ Find the Jeffreys prior, the posterior for $\alpha$ and ...
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### List of proper Jeffreys priors?

I know that Jeffreys priors are often improper. In fact, the only proper Jeffreys prior that I know is for the success probability in Bernoulli model (the prior arcsine). I am curious to know if there ...
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 vote
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### 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 ...
329 views

### Computing the Bayesian Estimator with Jeffreys prior for the Gamma distribution

Question: Let $X_1, · · · , X_n$ be a random sample from $Gamma(1, θ)$. The population mean is $θ$. Assume that the Jeffreys prior is used. Find the generalized Bayesian estimator of θ under the SEL (...
157 views

### How do I write the Jeffreys prior for error variances in stan? $p(\mu, \sigma_1^2, \dots, \sigma_C^2) \propto \Pi{ \sigma_i^{-2}}$ [closed]

I need to model the Jeffreys prior for error variances in a heteroscedastic ANOVA design in rstan. That is to say, $\pi(\mu,\sigma_1^2,\dotsb,\sigma_C^2)\varpropto\Pi_{i=1}^{C}\sigma_i^{-2}$. Is the ...
1 vote
214 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 ...