Alan Meeting
From 03/31, see below for more!
Outline
Title
On the ability to detect leading indicators of catastrophe in unreplicated time series
Introduction
Background on Warning Signals
 literature
 Saddle Node bifurcation
 Detecting decreasing stabilization  gradual vs changepoint estimation
Reasons detection can fail:
 Ergodicity: ensembles vs single instances
 Sufficient statistical power
 Appropriate dynamics
Methods
 Defining an indicator  significant Kendall rank correlation coefficient [math]\displaystyle{ \tau }[/math] as in doi:10.1073/pnas.0802430105
 Simulation approach
 Analytic limits
 accounting for delay?
Figures
 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
Towards a better approach
 Estimating the linear system directly:
 estimating the exponential coefficient [math]\displaystyle{ \lambda }[/math] of the autocorrelation function directly. Contrast to the autocorrelation. Estimating spectral width.
 estimating variance directly: [math]\displaystyle{ \frac{\sigma^2}{2\lambda } }[/math]
 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
 Warning Signals intro (Alan)
 Scope & previous work > 1D (Alan)
 Reasons Detection can fail (Carl)
 Methods > defining an indicator (Carl)
 Simulation approach (Carl)
 Analytic limits (Carl  still to do)
 Accounting for delay (Carl  still to do)
 Results  saddle node (Carl  still to do)
 Results  single replicate (Carl  still to do)
 Conclusions (Alan / both)
style guidelines
