How does marginalization impact the complexity of a Bayesian model?

Marginalization in the context of a Bayesian model is a process used to integrate out or eliminate certain variables from a model, allowing for the computation of probabilities relevant to other variables. When marginalization is applied, it doesn't simply reduce the model to a simpler form. Instead, it can lead to more complex interactions between the remaining variables within the model.

This occurs because marginalization involves summing over the probabilities of the eliminated variables, which can contribute to dependencies or interactions among the variables that remain. As a result, the remaining variables might exhibit more intricate relationships as their behavior becomes conditioned upon the absence of other variables, leading to a richer and potentially more complex joint distribution.

While marginalization can make computations simpler in some respects, the underlying relationships and dependencies among the remaining variables can become more complex as a result of the interactions introduced by conditioning on the removed variables. This aspect is crucial in understanding how marginalization can influence the dynamics and complexities of a Bayesian model.