User:Carl Boettiger/Notebook/Comparative Phylogenetics/2010/05/11

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Peter Meeting
Discussed potential solution to the model choice scenario:
 * Consider an ordered list of models, A, B, C, D
 * Then the Neyman-Pearson Lemma (see earlier entry on this) lets us walk through the list in the following fashion:  We generate the simulated data sets under model A and compare likelihood ratios in each case.  If the likelihood ratio of the observed data falls outside the 95% confidence interval, than it with this confidence that we are saying the data justify the alternate model (model B).  Then repeat, generating under model B and comparing to model C, and so forth until we cannot reject the simpler model.

More subtle concerns:
 * The model generating the data used in the bootstrap in an estimate, and shouldn't be treated as the true model with no uncertainty, but rather be bootstrapped itself.
 * Of course the method should consider probabilistic partitions of the data. The MLE partition alone will be misleading.