User:Carl Boettiger/Notebook/Stochastic Population Dynamics/2010/04/20

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 * style="background-color: #EEE"|[[Image:owwnotebook_icon.png|128px]] Stochastic Population Dynamics
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 * style="background-color: #F2F2F2" align="center"|  |Main project page


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Alan Meeting
From 03/31, see  below for more!

Towards a better approach

 * Estimating the linear system directly:
 * 1) estimating the exponential coefficient $$ \lambda $$ of the autocorrelation function directly.  Contrast to the autocorrelation.  Estimating spectral width.
 * 2) estimating variance directly: $$ \frac{\sigma^2}{2\lambda } $$
 * Compare to ARMA approach of #Ives2010 pmid=19849710


 * Changepoint analysis vs gradual trends.
 * i.e. web example,
 * book,
 * Bayesian / Dirchelet Process Prior analysis,
 * model selection.


 * Examples from software:
 * correlation C executable
 * R: source("warning_signals.R") example.

Other topics

 * F1000
 * Workstation order
 * Adaptive Dynamics manuscript
 * Labrids Manuscript

Updated Outline

 * 1) Warning Signals intro (Alan)
 * 2) Scope & previous work -> 1D (Alan)
 * 3) Reasons Detection can fail (Carl)
 * 4) Methods -> defining an indicator (Carl)
 * 5) Simulation approach (Carl)
 * 6) Analytic limits (Carl -- still to do)
 * 7) Accounting for delay (Carl -- still to do)
 * 8) Results -- saddle node (Carl -- still to do)
 * 9) Results -- single replicate (Carl -- still to do)
 * 10) Conclusions (Alan / both)

style guidelines


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