# how posterior function is calculated in JAGS

I have a theoretical question. I understand the JAGS samples from the posterior function of a model. But I don't understand (nor I can find in the documentation) how it calculates the posterior in the first place (the function from which it later samples from using Gibbs).
thank you very much Ariel

There's only one way of obtaining posterior distribution: by applying Bayes theorem. If your likelihood is $$f(X|\theta)$$ and the prior is $$g(\theta)$$, then the posterior is
$$g(\theta|X) \propto f(X|\theta)\, g(\theta)$$
where the normalizing constant $$f(X)$$ is ignored, because it is not needed for MCMC, or optimization.
For example, if you assume that $$X$$ is distributed according to binomial distribution with known $$n$$ and unknown $$p$$, and you assume uniform prior for $$p$$. So if you want to calculate posterior probability of observing some particular value of $$\theta$$, you multiply binomial portability mass function evaluated at your data point $$x$$, with parameters $$n$$ and $$p$$, and multiply it with uniform probability density function evaluated at $$\theta$$. No black magic involved.