*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 τ 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 λ of the autocorrelation function directly. Contrast to the autocorrelation. Estimating spectral width.
- estimating variance directly:

Compare to ARMA approach of

- Ziebarth NL, Abbott KC, and Ives AR. . pmid:19849710. PubMed HubMed [Ives2010]

- 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)