inst/examples/appendices/validating_approximation.md

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

In the case of the simulated model, we can compare our process of simulating under the approximate models, OU and LSN, to what we would have gotten if we could simulate under the true process.

Loading required package: earlywarning

Now we create the replicates by simulating under the original model. We will not try to estimate the nonlinear model first, as we generally do not have the power to do this well (but see my notes attempting this anyway).

require(populationdynamics)

Loading required package: populationdynamics

pars = c(Xo = 730, e = 0.5, a = 100, K = 1000, 
    h = 200, i = 0, Da = 0.09, Dt = 0, p = 2)
time = seq(0, 500, length = 500)
sn <- saddle_node_ibm(pars, time, reps = nreps)
X <- data.frame(time = time, value = sn$x1)

We tidy up the data a bit

require(reshape2)

Loading required package: reshape2

dat <- melt(sn$x1)
names(dat) = c("time", "rep", "population")

We can set up a parallel envirnoment for a multicore machine,

require(doMC)

Loading required package: doMC

Loading required package: foreach

Loading required package: iterators

Loading required package: codetools

Loading required package: multicore

registerDoMC()

We can now fit the LSN model to each of these replicates,

require(plyr)

Loading required package: plyr

models <- dlply(dat, "rep", function(X) {
    Y <- data.frame(X$time, X$population)
    stability_model(Y, "LSN")
}, .parallel = TRUE)

and look at the distribution of parameters.

p <- sapply(models, `[[`, "pars")

We compare this to simulating replicates from the approximate model and restimating parameters. We will use the model average parameters as the parameters for a model that will generate our simulations.

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