In cboettig/earlywarning: Detection of Early Warning Signals for Catastrophic Bifurcations

``` {r settings, echo=FALSE} opts_knit$set(cache=TRUE, upload.fun=socialR::flickr.url, message=FALSE, comment=NA)

# Model-based detection of early warning under a delay

What happens when we attempt to fit the linear change model to a signal in which the environment is initially constant and then begins degrading?

First let's simulate some such data

``` {r }
require(populationdynamics)
require(earlywarning)
pars = c(Xo = 500, e = 0.5, a = 180, K = 1000, h = 200,
    i = 0, Da = .45, Dt = 50, p = 2)
sn <- saddle_node_ibm(pars, times=seq(0,100, length=200))
X <- ts(sn$x1,start=sn$time[1], deltat=sn$time[2]-sn$time[1])

Observe that this produces timeseries has 200 points in the interval (0,100) with a linear change begining half way through, at Dt=50, where it begins approaching a saddle-node bifurcation. Let's fit both our models:

A <- stability_model(X, "OU")
B <- stability_model(X, "LSN")
observed <- -2 * (logLik(A) - logLik(B))
observed
````

... and then use the bootstrapped likelihood ratios to see if this difference is significant:

``` {r }
require(snowfall)
sfInit(parallel=TRUE, cpu=16)
sfLibrary(earlywarning)
sfExportAll()
reps <- sfLapply(1:100, function(i) compare(A, B))
lr <- lik_ratios(reps)
roc <- roc_data(lr)
save(list=ls(), file="delayed.rda")

Plot the likelihood ratio distribution with a line indicating the observed value. Also plot the ROC curve.

``` {r } require(ggplot2) ggplot(lr) + geom_density(aes(value, color=simulation)) + geom_vline(aes(xintercept =observed)) ggplot(roc) + geom_line(aes(False.positives, True.positives)) + geom_abline(aes(yintercept=0, slope=1), lwd=.2) ````

Is this a concern for the windowed approach? It still complicates the calculation of the correlation statistic used to demonstrate a statistically significant increase. We certainly would not advocate choosing the region "by eye" as it were where the increase appears and then testing the correlation on that segment alone -- that would guarentee bias. In principle this faces the same problem that the starting point needs to be known in advance.

cboettig/earlywarning documentation built on May 13, 2019, 2:07 p.m.