User:Carl Boettiger/Notebook/Stochastic Population Dynamics/2010/08/07

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Trying to make this show reading of the day, the script below shows only current reading: <html> <script type="text/javascript" src=""></script> <script type="text/javascript" src="'s%20shared%20items%22%2Cs%3A%22true%22%2Cn%3A%22true%22%2Cb%3A%22false%22%7D)%3Bnew%20GRC"></script> </html>

Friendfeed discussion on solving this: <html> <iframe src="" frameborder="0" height="400" width="650" style="border:1px solid #aaa"></iframe> </html>

Warning Signals

  • Implementing likelihood-based methods for early warning signals. Trying three models:

[math]\displaystyle{ \begin{align} dX =& (\theta_1 + \theta_2 X) dt + \theta_3 dW_t \\ dX =&(\alpha_0+\beta t) (\theta + X) dt + \sigma dW_t \\ dX =& \alpha(t) (\theta + X) dt + \sigma dW_t \end{align} }[/math]

To Do

  1. Simulation routine for custom equations (2, 3)
  2. Neyman-Pearson Likelihood ratio test method between models
  3. Simulation from actual population dynamics -- update warning signals method to return individual runs