Description Usage Arguments Details Value Author(s) Source See Also Examples
Poisson regression charts for the monitoring of surveillance time series.
1 2 3 |
disProgObj |
object of class |
control |
A list controlling the behaviour of the algorithm
|
This function implements the seasonal Poisson charts based on generalized likelihood ratio (GLR) as described in the SFB Discussion Paper 500. A moving-window generalized likelihood ratio detector is used, i.e. the detector has the form
N = inf(... >= c_gamma)
where instead of 1<= k <= n the GLR statistic is
computed for all k \in {n-M, …, n-Mtilde+1}. To
achieve the typical behaviour from 1<= k <= n use
Mtilde=1
and M=-1
.
So N is the time point where the GLR statistic is above the
threshold the first time: An alarm is given and the surveillance is
resetted starting from time N+1. Note that the same
c.ARL
as before is used, but if mu0
is different at
N+1,N+2,… compared to time 1,2,… the run length
properties differ. Because c.ARL
to obtain a specific ARL can
only be obtained my Monte Carlo simulation there is no good way to
update c.ARL
automatically at the moment. Also, FIR GLR-detectors
might be worth considering.
At the moment, window limited “intercept
” charts have not been
extensively tested and are at the moment not supported. As speed is
not an issue here this doesn't bother too much. Therefore, a value of
M=-1
is always used in the intercept charts.
survRes |
|
M. Hoehle with contributions by V. Wimmer
Poisson regression charts for the monitoring of surveillance time series (2006), Höhle, M., SFB386 Discussion Paper 500.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 | ##Simulate data and apply the algorithm
S <- 1 ; t <- 1:120 ; m <- length(t)
beta <- c(1.5,0.6,0.6)
omega <- 2*pi/52
#log mu_{0,t}
base <- beta[1] + beta[2] * cos(omega*t) + beta[3] * sin(omega*t)
#Generate example data with changepoint and tau=tau
tau <- 100
kappa <- 0.4
mu0 <- exp(base)
mu1 <- exp(base + kappa)
#Generate data
set.seed(42)
x <- rpois(length(t),mu0*(exp(kappa)^(t>=tau)))
s.ts <- create.disProg(week=1:length(t),observed=x,state=(t>=tau))
#Plot the data
plot(s.ts,legend=NULL,xaxis.years=FALSE)
#Run
cntrl = list(range=t,c.ARL=5, Mtilde=1, mu0=mu0,
change="intercept",ret="value",dir="inc")
glr.ts <- algo.glrpois(s.ts,control=c(cntrl))
lr.ts <- algo.glrpois(s.ts,control=c(cntrl,theta=0.4))
plot(glr.ts,xaxis.years=FALSE)
plot(lr.ts,xaxis.years=FALSE)
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