文档介绍：c21a, 5/13/1996 09:22
CHAPTER 21
REGRESSION AND LINEAR MODELS
Fitting a theoretical curv e to a set of data p oin ts is one of the mon statistical problems
faced b y scien tists, engineers, and economists. This eld is v ery large, b ecause there is no one
solution that applies to all cases. Instead, w eha v ea n um b er of quite di eren t problems, dep ending
on just what prior information w e had ab out the phenomenon b eing observ ed, the measuremen t
errors, and the unkno wn parameters.
A t the end of Chapter 8 w e noted brie
y some problems that ortho do x theory encoun ters here
b ecause of the dicult y in distinguishing b et w een \random" and \nonrandom" quan tities. Another
dicult yisev en more troublesome in practice.
Un w an ted P arameters
That di erences in the prior information can generate qualitativ ely di eren t mathematical problems
has, of course, b een w ell recognized in the v oluminous ortho do x literature. Some `sharp and drastic'
di erences can b e expressed adequately b y di eren tc hoices of a mo del (for example the judgmen t
that a certain parameter should or should not b e presen t at all). But some more `gen tle' di erences
in the prior information can b e expressed precisely only b y di erences in the corresp onding prior
probabilities within a mo del. Ortho do x theory , whic h do es not admit the existence of t