General Statistical Models
General Statistical Models The time has come to learn some theory. This is a preview of STAT 5101–5102. We don’t need to learn much theory. We will proceed with the general strategy of all introductory statistics: don’t derive anything, just tell you stuff. 3.1 Probability Models 3.1.1 Kinds of Probability Theory There are two kinds of probability theory. There is the kind you will learn in STAT 5101-5102 (or 4101–4102, which is more or less the same except for leaving out the multivariable stuff). The material covered goes back hundreds of years, some of it discovered in the early 1600’s. And there is the kind you would learn in MATH 8651–8652 if you could take it, which no undergraduate does (it is a very hard Ph. D. level math course). The material covered goes back to 1933. It is all “new math”. These two kinds of probability can be called classical and measure-theoretic , respectively. The old kind (classical) is still very useful. For every 1000 people who know a lot of pr