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

### Outline


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


  • Defining an indicator – significant Kendall rank correlation coefficient τ as in doi: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


  • Misleading indicators
  • Need for further exploration