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# determination of P(k,N,w)
pval <- function(k,N,w)
{
return((k/w-N-1)*b(k,N,w)+2*Gb(k,N,w))
}
# helper function
b<-function(k,N,w)
{
return(choose(N,k)*w^k*(1-w)^(N-k))
}
# helper function
Gb<-function(k,N,w)
{
sum<-0
for(i in k:N)
{
sum <- sum + b(i,N,w)
}
return(sum)
}
# If two significant overlapping windows were found, these windows are
# merged. If the windows do not overlap, two different windows are stored
# in a list
listadapt <- function(lcur,lnew)
{
if(length(lcur)==0)
{
lcur=lnew
return(lcur)
}
else
{
if(lnew[[1]][1]<=lcur[[length(lcur)]][2])
{
lcur[[length(lcur)]][2]<-lnew[[1]][2]
if(lcur[[length(lcur)]][3]>lnew[[1]][3])
{
lcur[[length(lcur)]][3] <- lnew[[1]][3]
}
return(lcur)
}
else
{
lcur<-append(lcur,lnew)
return(lcur)
}
}
}
# This method searches for data accumulations by shifting a window with
# window size <w> across the data and deciding at each position if there
# is a data accumulation. To test this, a scan statistic with significance
# level <sign.level> is used.
scanStatistic <- function(vect, w=0.25, sign.level=0.1)
{
temp<-vect
vect <-unlist(vect)
vsort <- sort(vect)
N <- length(vect)
range <- (max(vect)) - (min(vect))
windowsize <- range*w
N <- length(vect)
binarizeddata<-temp
res<-list()
lcur<-list()
# shift a fixed window over the data
# the window is moved from point to point
for(i in seq_along(vect))
{
start <- vsort[i]
stop <- vsort[i] + windowsize
k <- length(vect[(vect >= start) & (vect <= stop)])
p <- pval(k,N,w)
if(p>1)
{
p=0.99
}
if(p<=sign.level & p>0 & k >= (N*w-1) & k > 2)
{
res <- listadapt(res,list(c(start,stop,p)))
}
}
# if no accumulation for a fixed <sign.level> was found, the
# binarization is rejected, and we search for a accumulation
# with a higher sign.level.
if(length(res)==0)
{
while(TRUE)
{
sign.level=sign.level+0.05
if(sign.level>2)
{
binarizeddata<-(sapply(vect,function(x) 0))
return(list(bindata=binarizeddata,thresholds=NA,reject=TRUE))
}
for(i in seq_along(vect))
{
start <- vsort[i]
stop <- vsort[i] + windowsize
k <- length(vect[(vect >= start) & (vect <= stop)])
p <- pval(k,N,w)
if(p>1)
{
p=0.99
}
if(p<=sign.level & p>0 & k >= (N*w-1) & k > 2)
{
#res <- append(res,list(c(start=start,stop=stop,pval=p)))
res <- listadapt(res,list(c(start,stop,p)))
}
}
if(length(res)!=0)
break
}
reject<-TRUE
}
else
{
reject<-FALSE
}
# search the window with the smallest sign.level.
# this window is used for the binarization
min=1000
ind=0
for(i in seq_along(res))
{
if(res[[i]][3]<min)
{
ind=i
min=res[[i]][3]
}
}
# are more points on the left or on the right side
# of the window? Based on this, the binarization is performed
bigger <- length(vect[vect > res[[ind]][2]])
smaller <- length(vect[vect < res[[ind]][1]])
if(bigger > smaller)
{
threshold<-res[[ind]][2]
small<-tail(vsort[vsort<=threshold],n=1)
big<-vsort[vsort>threshold][1]
thres<-(big+small)/2
for(i in seq_along(vect))
{
if(vect[i]<=threshold)
{
binarizeddata[i]<-0
}
else
{
binarizeddata[i]<-1
}
}
}
else
{
threshold<-res[[ind]][1]
small<-tail(vsort[vsort<threshold],n=1)
big<-vsort[vsort>=threshold][1]
thres<-(big+small)/2
for(i in seq_along(vect))
{
if(vect[i]>=threshold)
{
binarizeddata[i]<-1
}
else
{
binarizeddata[i]<-0
}
}
}
return(list(bindata=binarizeddata,thresholds=as.numeric(thres),reject=reject))
}
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