In Bayesian inference, what is the primary purpose of marginalization?

In Bayesian inference, marginalization is a technique used to derive the probability distribution of a subset of variables from a larger joint distribution. This is achieved by integrating (summing) over the variables that are not of immediate interest. The primary purpose of marginalization is to focus on the distribution of specific variables, allowing researchers to analyze how these variables behave in the context of the overall model, without needing to consider every individual parameter or variable present in the model.

When you marginalize, you effectively reduce the complexity of your analysis by eliminating variables that do not have a direct influence on the outcome you are interested in. This is particularly useful in high-dimensional spaces, where considering every variable can complicate interpretations and inferences.

While other choices may relate to marginalization in different contexts—such as simplifying models or enhancing computational efficiency—they do not capture the core objective of marginalization in Bayesian analysis, which is to center the focus on the variables of interest by integrating out others. This makes it a fundamental practice in Bayesian statistics, as it helps to isolate specific insights from a broader set of data.