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Suppose we have some data points that we believe they follow $N(\mu, \sigma^2)$, and both parameters are unknown . I want to assign conjugate prior distributions on both $\mu$ and $\sigma^2$, and then obtain the posterior distribution. How this can be done in R?

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I guess your answer can be found in wikipedia http://en.wikipedia.org/wiki/Conjugate_prior. The conjugate prior is the Normal-inverse gamma with hyperparameters $\mu_0, \nu, \alpha$ and $\beta$.

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  • $\begingroup$ Thanks! But what is the R code to obtain the posterior distribution? $\endgroup$ – user9292 Jan 4 '13 at 4:23
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    $\begingroup$ The posterior distribution has the form given in the above Wiki link. You don't need to use R to find the posterior, although you can download the Normal-Gamma Package if you need to have the normal-gamma PDF or CDF in R. $\endgroup$ – caburke Jan 4 '13 at 4:40

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