Biomedical Engineering Reference
In-Depth Information
els R,
L
(
x
,R) is either 0 (if
x
is what that model happens to generate) or . Then,
once we have our data, and find a R that generates that and nothing but that, rear-
range the coding scheme so that
D
(R,2) = 1; this is always possible. Thus,
C
SC
(
x
,2) = 1 bit.
27. This does not contradict the convergence result of the last paragraph;
one of the not-too-onerous conditions mentioned in the previous paragraph is
that the coding scheme remain fixed, and we're violating that.
28. Technically, a given regular language (ยง3.6).
29. If I replace the random data by the
exact
log-normal probability distri-
bution over the same range, and do a least-squares fit to that, the
R
2
actually in-
creases, to 0.994.
30. Professors Drenzer and Farrell kindly shared their data with me, but the
figures and analysis that follow are my own.
31. Note that the log-normal curve fitted to the
whole
data continues to
match the data well even in the tail. For further discussion, omitted here for rea-
sons of space, see http://bactra.org/weblog/232.html.
32. In reading this literature, it may be helpful to bear in mind that by
"methodological individualism," social scientists mean roughly what biologists
do by "reductionism."
12.
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