Reading

Trying to make this show reading of the day, the script below shows only current reading:

Friendfeed discussion on solving this:

Warning Signals

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


- Model 3 is intended to be a changepoint analysis, where α(t) is piecewise constant. - I solved analytically the transition probability density in Model 2 on User:Carl Boettiger/Notebook/Stochastic Population Dynamics/2010/05/06, see this and the following entry. - Code implementations are in Structured Populations repository

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