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Jaynes Errata
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Chapter 9: Repetitive experiments: probability and frequency

  • p. 282, second line after (9.24): ``$\sum_{j}^{m}$'' should be `` $\sum_{j=1}^{m}$''.

  • p. 285, last paragraph: ``How many terms $T(n, m)$ are in the sum (9.39)?'' should probably be ``How many choices of $n_{1},\ldots,n_{m}$ are there that sum to $n$?'' or ``How large is the set $U$?''

  • p. 286, second half: ``$\log(W / n)$'' (both places) should be ``$\log(W) / n$''.

  • p. 289, section 9.8, first paragraph: ``From (9.28)and (9.29) we see...'' These equations don't seem to have anything to do with what follows.

  • p. 292, equation (9.78): `` $\partial / (\log(Z) \partial \lambda)$'' should be `` $\partial \log(Z) / \partial \lambda$''.

  • p. 297, equation (9.94): The preceding text, ``we express (9.88) in decibel units as in Chapter 4:'', is misleading, as $\psi_{B}$ is not $\psi_{\infty}$ for some hypothesis $H \in B_{m}$. To make sense of what follows in this section, use the equality

    \begin{displaymath}\psi_{B} = \psi_{\infty} + n \sum_{k} f_{k} \log(f_{k}). \end{displaymath}

  • p. 305, second paragraph: ``where $\psi_{i}$ depends only on the data and $H_{i}$ is non-negative over $C$'' should be ``where $\psi_{i}$ depends only on the data and $H_{i}$, and is non-negative over $C$''.

Miscellaneous commentary

  • p. 300, section 9.12: This criticism of the (Pearson) chi-squared statistic is both fair and exaggerated: Jaynes is correct, but (1) its sensitivity to small expected frequencies has been well rehearsed in many texts, including elementary treatments; (2) the alternative given here, the likelihood ratio chi-squared statistic, has long been available (since about 1930). [Contributed by Nick Cox.]
  • p. 304, first (partial) paragraph: Jaynes is correct, but dependence on published tables is totally avoidable given modern software, and practice is steadily swinging to citing P-values rather than using conventional levels such as 5% and 1%. [Contributed by Nick Cox.]

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