... special¹

The two-part messages are special in that, of the class of two-part messages, there is purposely an inefficiency in the second part of the message. The inefficiency arises because each entry in the codebook can be used to encode any data, not just the data that it is optimal for.

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... using²

If we use base-2 logarithms then the message length is measured in bits. Throughout the paper we use natural logarithms, so the message length is measured in $\log_e 2$ bits, or nits (Boulton and Wallace, 1970).

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... effect³

Assuming that the codebook entries are optimal for the given codebook size.

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... spaces⁴

We could also have parameter spaces with both continuous and discrete parameters, and of varying dimension.

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... extreme⁵

An example where this issue occurs can be seen in Figure 5 for the last segment of region 2. The last change-point looks to be superfluous.

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