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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)
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