Questions tagged [objective-bayes]
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Significance of parameterisation invariance of Jeffreys prior
I often hear it said that the Jeffreys prior is well-motivated because it is invariant under reparametrization. The proof of this is quite straight-forward (I know the proof on e.g., wiki). I'm a bit confused about what the proof really means,…
innisfree
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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 are other proper Jeffreys priors, and eventually…
Celi
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Using some objective priors (for unbounded space) in a Metropolis-Hastings MCMC
I'm doing some simulations using a M-H MCMC, and I was thinking of using some objective priors for some parameters. These parameters must be in $\mathbb{R}^+$. I was thinking of using $\pi(\theta)\propto 1$.
Are there any inconveniences? Should I…
An old man in the sea.
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Example of a uniform prior not being objective
The key feature of a truly objective prior is that it is invariant under change of variables. I understand this concept, however, I'm having a hard time finding a simple 1D or 2D example of when you might need to use something like Jeffreys prior…
Davey
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Location-scale parameter with non-informative (improper) prior : at what condition is the posterior proper?
Consider the setup:
Let $(X_i | \mu = m, \sigma = s)$ be a continuous random variable with pdf$$f_{X_i | \mu, \sigma}(x | m, s) = f_{X_i | \mu , \sigma}\big( \frac{x-m}{s} | 0,1 \big) \ s^{-1}, x \in \mathbb{R}$$ where $( \mu,\sigma)$ is a random…
Celi
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