- What do we mean by "Integrating out the parameters" in Marginal likelihood? Particularly in the posterior formula.
The marginal likelihood in a posterior formulation, i.e P(theta|data) , as per my understanding is the probability of all data without taking the 'theta' into account. So does this mean that we are integrating out theta? If that is the case, do we apply limits over the integral in that case? What are those limits?
Some people say that we can integrate the product of prior and likelihood to obtain the marginal likelihood. So how does this links in posterior formulation, which already has this product in numerator.?
Calculation of Marginal likelihood is ignored at times. Its a constant, that is not used usually. However, we don't call such approaches "Fully Bayesian". What kind of advantages does Full Bayesian provide if you are adding a constant.