Estimating early warning signals and tipping points in climate

Early warning signals for tipping are typically second order statistics, namely increasing variance
(loss of resilience) and increasing autocorrelation (critical slowing down). However, it is statistically challenging
to estimate these from non-stationary data, which is exactly the case for systems approaching tipping points.
Moreover, the systems are typically highly non-linear and noisy, and this even more so, the closer to the tipping
point. I will discuss such statistical challenges for estimating essential quantities and doing statistical inference
related to tipping systems.