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.
My lightning talk proposal to iEvoBio was accepted!
Still mostly working in the Stochastic Population Dynamics notebook this week.