Wrote summary function using bootstrap confidence intervals for the bootstraps of the likelihoods directly.
On interpreting the bootstraps of likelihoods directly:
The extent to which the distributions themselves are distinct provides an indication of the ability to distinguish between models on the given phylogenetic tree and the actual data. For instance, if the tree was a star tree and the data produced by either BM or OU1, then all distributions would fall on top of one another.
The extent to which the observed likelihood matches those produced by the bootstraps under that model gives an indication of how well that model is fitting the actual data.
May also be interesting to look at the bootstrap confidence intervals around theta parameters, to see if they are distinct.
observed likelihoods of BM & OU1 are indistinguishable from one another but outside the 95% confidence interval of the other distributions. The observed likelihoods lie easily within the distribution produced by those models for both BM & OU1.
Observed likelihood for OU2 falls within the bootstrap likelihoods produced under OU2.
Observed likelihood for OU3 and OU4 fall significantly below the likelihoods expected by data simulated under these models, suggesting that OU2 is indeed the best fit.
Comparative Phylogenetics
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