The Importance of Optimizing Marginal Likelihood's The asymptotic theory for maximum likelihood estimates justifies replacing uncertain parameters in a scientific model by their maximum likelihood estimates. In many cases, each measurement of a system introduces new model parameters that are also uncertain. The asymptotic theory (as the number of measurements increases) can not apply to the joint estimation of all of the parameters because the set of parameters being estimated is not fixed. On the other hand, if one integrates out the extra model parameters that correspond to each measurement, the set of parameters is fixed and the asymptotic theory can apply. This talk will present an example where the joint estimate of all the parameters does not converge to the true value for the parameters that are same for all the measurements. It will also show that the maximum marginal likelihood estimates for these parameters does converge to their true values.