Questions tagged [jeffreys-prior]

The tag has no usage guidance.

12 questions with no upvoted or accepted answers
Filter by
Sorted by
Tagged with
6
votes
0answers
91 views

How to construct “reference priors”?

I have been reading about noninformative priors. Two of the most popular priors of this kind seem to be the Jeffreys prior and the reference prior. The Jeffreys prior has a clear construction, being ...
3
votes
0answers
45 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 ...
2
votes
0answers
49 views

How to specify a new joint prior distribution restricted to (0,1) interval in WinBUGS?

I am doing some Bayesian analysis in OpenBUGS and I need to specify a joint prior distribution for parameters $\gamma_1$ and $\gamma_2$ (the Jeffreys prior related to my model), such that $$\pi(\...
2
votes
0answers
182 views

Jeffreys's prior for negative binomial regresion

For a negative biomial model, where $Y_i \sim \text{NegBin}(\mu_i, \kappa)$ $$\mu_i:=\log EY_i = \mathbf{x_i} \mathbf{\beta} + \log t_i,$$ is the form of Jeffreys's prior known/published in some way ...
2
votes
0answers
43 views

Equivalance of reference prior and Jeffreys prior for $d = 1$

There are a number of sources that mention that the reference prior is equivalent to Jeffreys prior for $d = 1$ (see e.g. https://people.eecs.berkeley.edu/~jordan/courses/260-spring10/lectures/...
2
votes
0answers
117 views

Understanding my posterior with an uninformative prior with a poisson likelihood. Am I thinking about this correctly?

I have a problem to which I am trying to apply a Bayesian model. My data is generated as follows \begin{align} N_i \mid \mu &\sim \text{Poisson}(\mu) \\ Y_i \mid N_i, \theta_i &\sim \text{...
2
votes
0answers
711 views

Sample Size Formula for Wilson Score, Clopper Pearson, and Jeffrey's

I am interested in finding the sample size formulas for proportions using the Wilson Score, Clopper Pearson, and Jeffrey's methods to compare with the Wald method. Also if anyone has code to replicate ...
2
votes
0answers
268 views

Is Independent jeffreys prior different from independent reference prior?

I have a model involving two scalar parameters $\theta_1$ and $\theta_2$ and derived the Jeffreys prior for $\theta_1$ and $\theta_2$ independently (so for, e.g. $\pi(\theta_1)$, setting in the ...
1
vote
0answers
42 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 ...
1
vote
0answers
119 views

Distribution for which the Jeffreys prior is Gaussian, log-normal, or exponential?

To be clear, I'm not looking for the Jeffreys prior on parameters of Gaussian, log-normal, or exponential distributions. I am, instead, looking for a probability distribution, which has one or ...
1
vote
1answer
67 views

Noninformative prior for variance

In Bishop's Pattern Recognition and Machine learning, he states that if you want a noninformative prior for scale,$$\int_A^Bp(\sigma)d\sigma = \int_{A/c}^{B/c}p(\sigma)d\sigma = \int_A^Bp\left(\frac{1}...
0
votes
1answer
74 views

Prior distributions letting a small sample “speak”

I’ve got a general question. Let k be a parameter which must be estimated. It lies within the interval $[a, b]$, $a$ and $b$ being finite real numbers. Let us further assume we dispose of a series ...