I am reading about the Monte Carlo method for the first time and I would like some clarification. Here is what I understand so far:
We are interested in the value of the parameter $\theta$. We take a random sample from the population that is characterized by $\theta$, and using the values of the sample in conjunction with our prior distribution for $\theta$, we determine a posterior distribution for $\theta$, given the values $y_1, ..., y_n$ from our sample.
I read that the next step of the process is to randomly sample $s$ values from the distribution $p(\theta|y_1,...y_n)$, and use these values to approximate $\theta$. My question is, why do we bother with this posterior sampling if we already know $p(\theta|y_1,...y_n)$?