I am trying to learn about the Beta Binomial for Bayesian style probability. So far I have:
$p(D|\theta)$ is the likelihood of the data set.
$D$ is the data set.
$p(\theta)$ is the prior probability of the parameter $h$ (I would use $\theta$ instead of $h$, but for this example I'd rather use discrete probability instead of continuous).
So the posterior distribution is proportional to the likelihood times the prior:
$p(\theta|D) \propto p(D|\theta) \times p(\theta)$
My question is this: suppose we first get a data set $D_1$, and we use it to obtain a posterior distribution. But then (like batch style learning), we obtain another data set $D_2$. We first calculate the distribution given $D_1$ using the above equation, but then how do we update $\theta$ before using the equation again to obtain the new posterior from $D_2$?
Thanks in advance