Notes

Value of information

1. Reed with uniform large noise, logistic map
2. Reed with uniform large noise
3. Reed with uniform small noise
4. Sethi with uniform small noise, logistic map.
5. Sethi with large noise Doesn’t work. hmm..
6. voi_sethi_parameters.md , running value of information setup but with small noise & logistic map. Whoops, this example solves uniform noise but simulates log-normal noise, which probably explains the positive effect of growth noise once again.
   
7. Corrected Sethi simulation small, uniform noise and logisitic map. Confirms Mike’s hypothesis that the benefit to growh noise came from the assymetry of the log-normal noise, as the benefit is gone in this case. The policy functions all look like constant escapement rules, as expected for the “all low” noise limits.

Re-running with larger noise.
Also ran original value of information with gaussian noise.

Critical transitions and early warning

• Example with underlying critical transition externality
• added calculation of warning signals and distribution of resulting stats, and shows the state equation from May (1977).
• May (1977) example of transitions in optimal management without any deterioration of environment / approaching shifts.

• Conservative strategy that optimizes iteratively after selecting fraction P of optimal harvest level. Compare results with cautious strategy to the results for optimal harvest where P = 1

• Next, use specific distribution and probabilities of a transition (ROC curve). See table, eqn

1. Simulate timeseries before management begins, use this data to compute warning signals.
   
2. Calculate the ROC curve
3. Calculate the expected profits remaining under the hypothesis that the system is not going to collapse. “D”
4. Calculate the expected profits under the assumption that the system collapses (in the next timestep?) “C” == 0
5. Calculate the profits expected under a response to the signal. (Say, 50% reduction in harvest). “A”, “B”

Ideal response with complete information: determine the optimal policy under temporally changing f.

Proposed edits to the earlywarnings package

• separate out / functionalize each signal in generic_ews, separate plotting from evaluating.