Explain Marginalization More Intuitively

[farhanhubble]

For someone like me who does not yet possess the visual muscle, this article is incredibly valuable. For example, the easy-to-visualize explanation of conditioning as taking a slice of the distribution is great.

When it comes to marginalization, there is a little disconnect between the process of integrating with respect to one of the variables and the visual representation in the figure. I think it's important for the reader to visualize how the marginalization of a bivariate distribution produces a univariate distribution.

Suggested explanation:

Marginalization can be seen as first performing conditioning for each possible value(probability) of the variable being marginalized out. Each conditioning operation produces a distribution with that variable removed. In the second step, all such (infinitely many) distributions are squashed together by weighing them by their conditioning probabilities and summing them up, or integrating them with respect to the marginalized variable.

The slicing and adding operation can be visualized then to represent a crisp picture of the process.