bootstrap_and_CI function

Bootstrap and Confidence Interval

Not for sparse models and only for histograms

bootstrap_and_CI(sol, Time, R, alpha = 0.05, nbcores = 1, d_part = 5,
  n_perturb = 10, perc_perturb = 0.2, directed, filename = NULL)

Arguments

• sol: sol

• Time: time

• R: Number of bootstrap samples

• alpha: Level of confidence : $1- \alpha$

• nbcores: Number of cores for parallel execution

  If set to 1 it does sequential execution

  Beware: parallelization with fork (multicore) : doesn't work on Windows!

• d_part: Maximal level for finest partitions of time interval [0,T], used for kmeans initializations.

  • Algorithm takes partition up to depth $2^d$ with $d=1,...,d_{part}$
  • Explore partitions $[0,T], [0,T/2], [T/2,T], ... [0,T/2^d], ...[(2^d-1)T/2^d,T]$
  • Total number of partitions $npart= 2^{(d_{part} +1)} - 1$

• n_perturb: Number of different perturbations on k-means result

• perc_perturb: Percentage of labels that are to be perturbed (= randomly switched)

• directed: Boolean for directed (TRUE) or undirected (FALSE) case

• filename: filename

Examples

# data of a synthetic graph with 50 individuals and 3 clusters

n <- 50
Q <- 3

Time <- generated_Q3$data$Time
data <- generated_Q3$data
z <- generated_Q3$z

Dmax <- 2^3

# VEM-algo hist
sol.hist <- mainVEM(list(Nijk=statistics(data,n,Dmax,directed=FALSE),Time=Time),
     n,Qmin=3,directed=FALSE,method='hist',d_part=1,n_perturb=0)[[1]]

# compute bootstrap confidence bands
boot <- bootstrap_and_CI(sol.hist,Time,R=10,alpha=0.1,nbcores=1,d_part=1,n_perturb=0,
     directed=FALSE)

# plot confidence bands
alpha.hat <- exp(sol.hist$logintensities.ql)
vec.x <- (0:Dmax)*Time/Dmax
ind.ql <- 0
par(mfrow=c(2,3))
for (q in 1:Q){
  for (l in q:Q){
    ind.ql <- ind.ql+1
    ymax <- max(c(boot$CI.limits[ind.ql,2,],alpha.hat[ind.ql,]))
    plot(vec.x,c(alpha.hat[ind.ql,],alpha.hat[ind.ql,Dmax]),type='s',col='black',
        ylab='Intensity',xaxt='n',xlab= paste('(',q,',',l,')',sep=""),
        cex.axis=1.5,cex.lab=1.5,ylim=c(0,ymax),main='Confidence bands')
    lines(vec.x,c(boot$CI.limits[ind.ql,1,],boot$CI.limits[ind.ql,1,Dmax]),col='blue',
        type='s',lty=3)
    lines(vec.x,c(boot$CI.limits[ind.ql,2,],boot$CI.limits[ind.ql,2,Dmax]),col='blue',
        type='s',lty=3)
  }
}