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Pardon my ignorance, i am new to Bayesian Analysis.

I am trying to use Normal prior for a binomial likelihood, which of these are most likely candidates ( $\bar{x} $, $ \mu $, $ \sigma $ ) for prior and most likely candidates for constants ? Please advise.

Tyrone Williams
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    $\bar{x}$ is not a parameter of the normal distribution (it's the maximum-likelihood estimate of $\mu$) – Patrick Coulombe Aug 18 '14 at 03:41
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    It seems to me like your question does not make much sense as it stands now. Perhaps you'd benefit from reading introductory chapters/papers to the Bayesian approach. – Patrick Coulombe Aug 18 '14 at 04:40

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If the likelihood follows a binomial distribution, your conjugate prior is the beta distribution. Please check this great answer on the intuition of beta distribution.

After reading that answer, note that Beta(a, b) distribution can be approximated by the Normal distribution when a and b are sufficiently large.

You can play with a Beta distribtuion on this link. As you incraese a and b, the pdf looks more and more like the normal distribution.

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Zhubarb
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