SMML - Binomial |
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Strict Minimum Message Length (SMML) inference partitions the data space. Problem:
Given N, devise an optimal code for a two-part message to transmit
For this problem there is a polynomial-time algorithm (equivalent to Dijkstra's shortest-paths algorithm) to find an optimal partition of [0..N] and so construct an optimal code-book (Farr & Wallace 1997, 2002). Assuming a uniform-prior on the parameter
For a given number of trials, N, the program calculates the expected code length under an adaptive code, and, for MML, the optimal MML code book and the expected message length when using that code book. The latter is necessarily very slightly greater than that of the adaptive code because an MML message transmits not only the data but also something more, that is an opinion (inference, estimate) about the data.
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