
Basic statistical concepts 31
conditionally independent given f.
Unconditional independence of g and y
(p(g, y) = p(g)p(y)) does not imply they are also conditionally independent
(when the true value f is known) and vice versa.
The definitions are somewhat abstract and therefore we now put these ideas
in some more intuitive context.
Notation First let’s introduce a symbol ⊥ which indica tes the indepen-
dence and therefo re g ⊥ y is read as g is independent of y. If g and y ar e
depe ndent, that will be indicated simply by ‘not g ⊥ y’. The co nditio nal
independenc e and dependenc e of g and y given f are indicated by g ⊥ y|f
and ‘not g ⊥ y|f’, respectiv ...