Marginalization in Gaussian Distribution

Marginalization is a fundamental operation in probability and statistics that involves integrating out or summing over a variable to obtain the probability distribution of the remaining variables. When dealing with Gaussian distributions, marginalization is a straightforward process because the Gaussian distribution is closed under marginalization and conditioning operations.

Let’s consider a joint Gaussian distribution of two random variables X and Y:

p(X, Y) ~ N(μ, Σ)