Figure 6.

Optimal number of pseudocounts, m, as a function of the number of independent observations, n. Using the data listed in Table 3 and the method illustrated in Figure 5, we found the optimal number of pseudocounts for varying n. The method cannot be valid for n < 212 (vertical dotted line), because the calculated decrease in model description length for is greater than the description length of the model at , but it is not possible for a model to have a negative description length. For n between 212 and 1000, the calculation suggests we use a nearly constant number m of pseudocounts, roughly 19.4. In the limit of very large n, the MDL principle suggests the number of pseudocounts should grow proportionately to n^1/3.