This Repository contains the INLA.ews package for Bayesian detection of early warning signals.
When a dynamical system approaches a bifurcation point the state variable exhibits increased correlation and variance, this is known as critical slowing down. Our model assumes that the memory coefficient increases linearly as a function of time, and uses the R-INLA package to obtain the posterior marginal distributions. Of particular interest is the slope parameter which indicate whether or not correlation is increasing.
INLA.ews currently supports time-dependent AR(1) and fGn processes, although the latter is far more computationally costly.
You can install the development version of INLA.ews from GitHub with:
# install.packages("devtools")
devtools::install_github("eirikmn/INLA.ews")This is a basic example which shows you how to use the package to perform Bayesian analysis of a simulated time series which exhibit early warning signals in the form of increasing correlation.
library(INLA.ews)
# Set seed and parameters
set.seed(0)
n = 1000
sigma = 1
a=0.2
b=0.7/n
time = 1:n
phis = a+b*time
# Simulate time dependent process
data=numeric(n)
data[1] = rnorm(1,mean=0,sd=sigma)
for(i in 2:n){
data[i] = rnorm(1, mean=phis[i]*data[i-1],sd=sigma)
}
# Run inla.ews
object = inla.ews(data,model="ar1", memory.true=phis)The plot below shows the estimated posterior marginal mean for the lag-one correlation coefficient (blue) in the above example, with 95% credible intervals included (red). The black line represents the ‘true’ development of the memory.
This code is associated and written for an upcoming paper. Feel free to use the code, but please cite the accompanying paper (when it is published).
The code in this repository is made available under the terms of the GNU General Public License (GPL) version 2 License. For details, see LICENSE.md file.