# Questions tagged [jeffreys-prior]

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### 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 ...
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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 ...
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 $$\pi(\... 0answers 182 views ### Jeffreys's prior for negative binomial regresion For a negative biomial model, where Y_i \sim \text{NegBin}(\mu_i, \kappa)$$\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 ... 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/... 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{... 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 ... 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 ... 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 ... 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 ... 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}...
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 ...