# Bootstrap and Confidence Interval Not for sparse models and only for histograms ```r 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 ```r # 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) } } ```

bootstrap_and_CI function