Prior vs. Marginal Probabilities What is the difference between prior and marginal probabilities in layman terms? Do these concepts refer to the same thing, but in the different contexts?
 A: Somewhat sloppy definitions:
Marginal probability
You have two dice. Let $X$ be a random variable denoting the roll of the first die. Let $Y$ be a random variable denoting the roll of the second die.
Let $P(X=x,Y=x)$ be a function giving the probability that $X=x$ and $Y=y$. $P$ is called the joint probability mass function. This function defines the joint probability distribution over the two dice rolls.
$P(X=x)$ is called a marginal probability. You come to a marginal probability by summing or integrating the joint probability distribution.
$$ P(X=x) = \sum_{y=1}^6 P(X=x, Y=y) $$
Eg. The probability your first die roll is a 2 is the probability you rolled 2 and a 1 plus the probability you rolled a 2 and a 2 plus the probability you rolled a 2 and a 3 etc... 
Basically, the joint probability distribution is the distribution over all your random variables. And a marginal probability distribution is a distribution that's over fewer than all your variables.
Bayesian Prior
Let $\theta$ be some parameter that represents your beliefs, some prior beliefs before you see the data. $P(\theta)$ is called a prior.
A: The prior, denoted $P(\omega)$, denotes the probability of some event $\omega$ even before any data has been taken.   
A marginal distribution is rather different.  You hold a variable value and integrate over the unknown values.
