Validate parameter identifiabiltiy by speciation models

[MathiasRenaud]

• [x] Yule model
• [x] birth-death models

[MathiasRenaud]

Yule model - Lambda (target tree: lambda=0.1)

[MathiasRenaud]

Birth-death - Lambda (target tree: lambda=0.1, mu=0.003)

[MathiasRenaud]

Less identifiability for Mu param with Birth-death so far, but still trying different settings/distributions. (lambda = 0.1, mu = 0.003).

[ArtPoon]

For the plot of mu under the birth-death model, please change range of y-axis to make the differences visible, and apply log-transformation to x-axis (also may want to sample some points at very low values of mu).

Also check for confounding of lambda and mu.

[MathiasRenaud]

mu under the birth-death model with log-transformed x-axis and smaller y-axis range.

[MathiasRenaud]

Here is a heat map showing the kernel distance from obs.tree (lambda=0.1) for each pairwise combination of lambda and mu simulated under the birth-death model.

The script for building the matrix and plotting the heatmap are in pkg/examples/example-bd.R.

[ArtPoon]

Based on this grid search, it looks like lambda and mu are somewhat confounded with a positive association between the two, which is what I would have expected. See how SMC does on some test cases, now that we can be aware of this. Also need to have finer granularity with lambda on grid (twice as many points) and enforce lambda > mu. Once we have that result then it is ok to close this issue.

[MathiasRenaud]

Dotted lines indicate true values of lambda (0.1) and mu (0.003)