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My data is a set of $N$ observations $y_i$.

I would like to estimate $\mu$ and $\sigma$ in the following model:

$y_i \sim \mathrm{Normal}(\theta, \sigma)$

$\theta \sim \mathrm{Normal}(\mu, \frac{\sigma}{N})$

$\mu \sim \mathrm{Normal}(??, ??)$

$\sigma \sim ???(??,??)$

I would like to perform an Empirical Bayes analysis. Would someone be able to help me and explain how I would go about parametrizing the priors for empirical bayes?

user1375871
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    Just a shameless plug for a new MCMC package in julia: https://github.com/brian-j-smith/Mamba.jl The documentation is very extensive and includes many examples from the BUGS manual. – bdeonovic Jun 22 '14 at 21:41
  • @Benjamin how is it different from the basic MCMC package? – shadowtalker Jun 22 '14 at 22:38
  • It is very flexible package; the MCMC package relies on a modeling language, which makes it easier (less verbose?), or simpler to do bayesian inference, but more constrained in the things you can do. Also the Mamba package has many samplers coded up (MCMC only has 1 I believe), allows for different samplers to be used for different variables (i.e. blocking), and will be parallelized in an up coming release :) – bdeonovic Jun 23 '14 at 01:11

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