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The integration process in marginalization is fundamentally about reducing the complexity of a joint probability distribution by focusing on specific variables of interest. This involves summing or integrating over the values of the other variables to obtain a marginal distribution.

When you marginalize, you essentially want to find the probability of a subset of variables while ignoring the rest. For instance, in a joint distribution of multiple random variables, to find the marginal distribution of one variable, you sum (for discrete variables) or integrate (for continuous variables) over the other variables.

This approach allows for a clear understanding of the behavior of the variable of interest without needing to consider the entire joint distribution, making it a crucial concept in probability theory, statistics, and relevant areas in AI.

The other options refer to different concepts in probability and statistics. Multiplying probability distributions together corresponds to finding joint distributions rather than marginalization. Using prior knowledge to adjust likelihoods pertains more to Bayesian inference. Performing regression analysis involves modeling relationships between dependent and independent variables, which is not related to the marginalization process.