There are more possibilities open to you when using maximum likelihood estimation than you might think.
When we're conducting inference, it's often the case that our primary interest lies with a sub-set of the parameters. and the other parameters are essentially what we call "nuisance parameters". They're part of the data-generating process, but we're not that interested in learning about them.
When we're conducting inference, it's often the case that our primary interest lies with a sub-set of the parameters. and the other parameters are essentially what we call "nuisance parameters". They're part of the data-generating process, but we're not that interested in learning about them.
We can't just ignore these other parameters - that would amount to mis-specifying the model we're working with. However, in the context of maximum likelihood estimation, there are several things that we can do to make life a little easier.