Which mathematical operation is commonly used in the marginalization process?

In the context of probabilistic models and inference, marginalization refers to the process of summing or integrating over the values of one or more variables to derive the marginal distribution of a subset of variables. The operation commonly employed in this context is integration, particularly when dealing with continuous random variables.

When you integrate over the probability space, you effectively consider all possible values of the variable(s) being marginalized out, thus obtaining a distribution that only includes the remaining variables. This is critical in Bayesian inference, where we often need the marginal distribution of a parameter or data given the evidence by integrating out other parameters or latent variables.

This mathematical operation allows for the reduction of complex distributions into more manageable forms, making it possible to focus on specific aspects of the data while still accounting for the uncertainty introduced by the variables that were integrated out.