User:Carl Boettiger/Notebook/Stochastic Population Dynamics/2010/03/31

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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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Research
Writing up work just on ensemble vs single instance detection of regime shifts. See this entry

Outline
Title

On the ability to detect leading indicators of catastrophe in unreplicated time series

Introduction Background on Warning Signals Reasons detection can fail: Methods Figures
 * 1) literature
 * 2) Saddle Node bifurcation
 * 3) Detecting decreasing stabilization -- gradual vs changepoint estimation
 * 1) Ergodicity: ensembles vs single instances
 * 2) Sufficient statistical power
 * 3) Appropriate dynamics
 * Defining an indicator -- significant Kendall rank correlation coefficient $$\tau$$ as in 10.1073/pnas.0802430105
 * Simulation approach
 * Analytic limits
 * accounting for delay?
 * Saddle node bifurcation example -- should discuss difference between stochastic and deterministic edge?
 * Single replicates using standard detection statistics

Results/Discussion
 * Misleading indicators
 * Need for further exploration


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