How can the parameters be unknown but the probability distribution be known? In an article (Nelson & Katzenstein, 2014) I came across the following sentence: ... “a fixed model of the economy with known parameters (or sometimes unknown parameters with known probability distributions).” (p. 380). I was wondering how the parameters can be unknown while the probability distributions are known. To my understanding, knowing a probability distribution entails knowing the parameters (the mean and variance). Can you help me reconcile this?
 A: When I took a mathematical statistics class, when talking about such as estimating the mean and variance of a normal distribution, the instructor always said we had a family of distributions. Every distribution in the family is normal, but with a different mean and variance. So what we assume at the beginning of the problem is not that we know the distribution, but rather that we know the distribution is a member of this family.
Outside of a mathematical statistics class, people do not speak as carefully. I would say that the paper you are reading is speaking loosely, and what is really meant is that you assume that the true model is in a particular family of models. And furthermore, that this family is parametrized: you can get from a list of numbers (the values of the parameters) to a model in the family, and back.
I think it's fine to speak that loosely in an economics paper for a professional audience, in order to meet wordcount, but it certainly is confusing for students, and I think classroom settings should be more precise, the way mine was.
