Appendices
Working on Appendices
Ergodicity
Null of Kendall’s tau/rank correlations – independence of X and Y, not satisfied even over replicates. Adjusted codes to use Pearson’s (default option, need to pass option up to higher-level functions). Repeated Figure 2 plots with Pearson’s, results not much different, funny multimodal though:
Actually verifying independence is rather more challenging, though convenient in this case that a test such as Pearson’s is not designed to do this, see https://en.wikipedia.org/wiki/Brownian_covariance
Calculating Error
Still to write. Figures with shading, management angle. References to management of risk?
Models
Wrote section, still could use panel figure on models.
For each model: Graph of birth rate and death rate, with several overlays showing parameter change. Graph of net growth rate. Graph of linearized system. bifurcation plot. energy landscape. Earlier entries for starting point on this.
Likelihood Calculations
Wrote section.
Model Choice
Model choice between LTC and LSN for examples. 
- Comments on model adequacy.
Examples
Still assembling.
- Should probably focus on empirical examples.
- Could do simulated data not from LTC/LSN dynamics.
- Should include LTC dynamics on some models.
- Include Drake data?
- Include CaCO3 data?
- Kendall’s tau estimates for Deut I, II, III. (III already done, just for comparison. IV throws error exceptions).
- Other deuterium runs show much the same story, very little power in the correlation statistics and even clearer detection of models:
A bit surprising given model parameters show very slow rate of change (though over a long interval), and given how poorly even the variance indicator does.
Misc
Moved into LaTeX as well to get sense of length, though will be difficult to edit two copies. Writing appendix in LaTeX for simplicity.
Stats stack-exchange: https://stats.stackexchange.com/