This page contains errata for the MDL Tutorial, which appeared as
P.D. Grünwald, A tutorial introduction
to the minimum description length principle (80 pages), Chapter 1 and 2 in the collection
Advances in Minimum Description Length: Theory and Applications
(edited by P. Grünwald, I.J. Myung, M. Pitt), MIT
Press, April 2005.
A preliminary version appeared in the CoRR archive (the computer
science branch of the physics arXiv) under code math.ST/0406077. This is also the version that can be found on my homepage; that is, here.
ERRATA for the on-line/CoRR version
The following errata are only present in the on-line version and not
in the Advances book.
- The definition of Fisher information on page 48 is incorrect: log
(logarithm to base 2) should be replaced by ln (logarithm to
base e). Note however that, perhaps confusingly, (2.21) on
page 47 is correct: there the log should indeed be
taken to base 2.
ERRATA for both the book version and the on-line/CoRR version
The following errata are present both in the on-line version and
in the Advances book.
- Section 2.2.2, Example 2 (Page 27, 6th line of the on-line
version): inside the summation from 1 to m, 2^m should be 2^i.
- Equation 2.4 (Page 29 of both the on-line version and the book):
the sum should be taken over (calligraphic) Z, not X.
- Example 2.5 (Page 30 of both on-line version and book): after the
first equal ("=") sign in the equation inside the example, a minus
("-") should be added.
- Example 2.8,
Equation 2.8 (Page 36 both in the book and the online version): the k in front of k log (n+1)
should be k' rather than k (it's the number of parameters, not
the Markov chain order).
- Similarly, in Equation (2.9), the k refers to the number of
parameters, so in the context of Example 2,8, it should be called k'
(in later sections, k is used for number of parameters).
- In Example 2.8, Equation (2.8), one might argue that there should also be an extra
term of size k. This is the number of bits needed to encode
the starting state of the chain.
- The calculations in Example 2.17 (page 48 in both the on-line
version and the book), are incorrect. To add to the
confusion, the calculation in the book is different from the
calculation in the on-line version; yet both are incorrect!
The right calculation is as follows: the
Fisher information is given by 1/t(1-t)
(with t replaced by "theta"; in the on-line version it was
wrongfully stated that the Fisher information is t(1-t)). The integral
over the square root of the Fisher information from 0 to 1
thus should really be π (and not π/8, as claimed in the
on-line version, or 2, as claimed in the book). Thus, the
correct calculation of COMP(M) gives
COMP(M) = 0.5log n + 0.5 log (0.5 π) + o(1).
Last updated: April 2006. Thanks to Wouter Koolen, Kinh Tieu, Michal
Przykucki and Chris Sims for pointing out
some of these mistakes.
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