backprojNP(sts, incu.pmf, 
   control = list(k = 2, 
                  eps = rep(0.005,2), 
                  iter.max=rep(250,2), 
                  Tmark = nrow(sts), 
                  B = -1, 
                  alpha = 0.05, 
                  verbose = FALSE, 
                  lambda0 = NULL,
                  eq3a.method = c("R","C"),
                  hookFun = function(stsbp) {}),
     ...)

#Generate an artificial outbreak of size n starting at time t0 and being of length
n <- 1e3 ; t0 <- 23 ; l <- 10

#PMF of the incubation time is an interval censored gamma distribution
#with mean 15 truncated at 25.
dmax <- 25
inc.pmf <- c(0,(pgamma(1:dmax,15,1.4) - pgamma(0:(dmax-1),15,1.4))/pgamma(dmax,15,1.4))
#Function to sample from the incubation time
rincu <- function(n) {
  sample(0:dmax, size=n, replace=TRUE, prob=inc.pmf)
}
#Sample time of exposure and length of incubation time
set.seed(123)
exposureTimes <- t0 + sample(x=0:(l-1),size=n,replace=TRUE)
symptomTimes <- exposureTimes + rincu(n)

#Time series of exposure (truth) and symptom onset (observed)
X <- table( factor(exposureTimes,levels=1:(max(symptomTimes)+dmax)))
Y <- table( factor(symptomTimes,levels=1:(max(symptomTimes)+dmax)))
#Convert Y to an sts object
Ysts <- sts(Y)

#Plot the outbreak
plot(Ysts, xaxis.labelFormat=NULL, legend=NULL)
#Add true number of exposures to the plot
lines(1:length(Y)+0.2,X,col="red",type="h",lty=2)


#Helper function to show the EM step
plotIt <- function(cur.sts) {
  plot(cur.sts,xaxis.labelFormat=NULL, legend=NULL,ylim=c(0,140))
}

#Call non-parametric back-projection function with hook function but
#without bootstrapped confidence intervals
bpnp.control <- list(k=0,eps=rep(0.005,2),iter.max=rep(250,2),B=-1,hookFun=plotIt,verbose=TRUE)

#Fast C version (use argument: eq3a.method="C")! 
sts.bp <- backprojNP(Ysts, incu.pmf=inc.pmf,
    control=modifyList(bpnp.control,list(eq3a.method="C")), ylim=c(0,max(X,Y)))

#Show result
plot(sts.bp,xaxis.labelFormat=NULL,legend=NULL,lwd=c(1,1,2),lty=c(1,1,1),main="")
lines(1:length(Y)+0.2,X,col="red",type="h",lty=2)

#Do the convolution for the expectation
mu <- matrix(0,ncol=ncol(sts.bp),nrow=nrow(sts.bp))
#Loop over all series
for (j in 1:ncol(sts.bp)) { 
  #Loop over all time points
  for (t in 1:nrow(sts.bp)) {
    #Convolution, note support of inc.pmf starts at zero (move idx by 1)
    i <- seq_len(t)
    mu[t,j] <- sum(inc.pmf[t-i+1] * upperbound(sts.bp)[i,j],na.rm=TRUE)
  }
}
#Show the fit
lines(1:nrow(sts.bp)-0.5,mu[,1],col="green",type="s",lwd=3)

#Non-parametric back-projection including boostrap CIs. B=10 is only
#used for illustration in the documentation example
#In practice use a realistic value of B=1000 or more.
bpnp.control2 <- modifyList(bpnp.control, list(hookFun=NULL,k=2,B=10,eq3a.method="C"))
## Not run: 
bpnp.control2 <- modifyList(bpnp.control, list(hookFun=NULL,k=2,B=1000,eq3a.method="C"))

## End(Not run)
sts.bp2 <- backprojNP(Ysts, incu.pmf=inc.pmf, control=bpnp.control2)

######################################################################
# Plot the result. This is currently a manual routine.
# ToDo: Need to specify a plot method for stsBP objects which also
#       shows the CI.
#
# Parameters:
#  stsBP - object of class stsBP which is to be plotted.
######################################################################

plot.stsBP <- function(stsBP) {
  maxy <- max(observed(stsBP),upperbound(stsBP),stsBP@ci,na.rm=TRUE)
  plot(upperbound(stsBP),type="n",ylim=c(0,maxy), ylab="Cases",xlab="time")
  if (!all(is.na(stsBP@ci))) {
    polygon( c(1:nrow(stsBP),rev(1:nrow(stsBP))),
             c(stsBP@ci[2,,1],rev(stsBP@ci[1,,1])),col="lightgray")
  }
  lines(upperbound(stsBP),type="l",lwd=2)
  legend(x="topright",c(expression(lambda[t])),lty=c(1),col=c(1),fill=c(NA),border=c(NA),lwd=c(2))

  invisible()
}

#Plot the result of k=0 and add truth for comparison. No CIs available
plot.stsBP(sts.bp)
lines(1:length(Y),X,col=2,type="h")
#Same for k=2
plot.stsBP(sts.bp2)
lines(1:length(Y),X,col=2,type="h")