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

1. literature
2. Saddle Node bifurcation
3. Detecting decreasing stabilization – gradual vs changepoint estimation

Reasons detection can fail:

1. Ergodicity: ensembles vs single instances
2. Sufficient statistical power
3. 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