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scanstat.Rmd
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scanstat.Rmd
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---
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title: "scanstat"
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output: pdf_document
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date: '2022-05-09'
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---
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```{r setup, include=FALSE}
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knitr::opts_chunk$set(echo = TRUE)
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```
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```{r}
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library("localScore")
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library("latex2exp")
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library("Rcpp")
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library("caret")
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library("ROCR")
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```
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```{r}
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PoissonProcess <- function(lambda,T) {
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return(sort(runif(rpois(1,lambda*T),0,T)))
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}
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```
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```{r}
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SimulationH1 <- function(lambda0, lambda1,T,tau){
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ppH0=PoissonProcess(lambda0,T)
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ppH1.segt=PoissonProcess(lambda1,tau)
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dbt=runif(1,0,T-tau)
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ppH0bis=PoissonProcess(lambda0,T)
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ppH1.repo=dbt+ppH1.segt
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ppH0_avant=ppH0bis[which(ppH0bis<ppH1.repo[1])]
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ppH0_apres=ppH0bis[which(ppH0bis>ppH1.repo[length(ppH1.repo)])]
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ppH1=c(ppH0_avant,ppH1.repo,ppH0_apres)
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return (ppH1)
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}
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```
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```{r}
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TimeBetweenEvent <- function(pp){
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n=length(pp)
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tbe=pp[2:n]-pp[1:n1-1]
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tbe=c(0,tbe)
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return (tbe)
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}
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DataFrame <- function(pp,tbe){
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list=data.frame(ProcessusPoisson=pp, TimeBetweenEvent=tbe)
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}
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```
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```{r}
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ScanStat <- function(pp, T, tau){
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n=length(pp)
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stop=n-length(which(pp>(T-tau)))
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ScanStat=0
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for (i in (1:stop)) {
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x=which((pp>=pp[i])&(pp<=(pp[i]+tau)))
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scan=length(x)
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if (scan>ScanStat) {ScanStat=scan
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max=i}
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}
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return (c(max,ScanStat))
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}
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```
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```{r}
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EmpDistrib <- function(lambda, n_sample,T,tau){
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pp=PoissonProcess(lambda,T)
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scan=c(ScanStat(pp,T, tau)[2])
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index=c(ScanStat(pp,T, tau)[1])
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for (i in 2:(n_sample)){
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pp=PoissonProcess(lambda,T)
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scan=rbind(scan,ScanStat(pp,T, tau)[2])
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index=rbind(index,ScanStat(pp,T, tau)[1])
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}
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min_scan=min(scan)-1
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max_scan=max(scan)
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table1=table(factor(scan, levels = min_scan:max_scan))
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EmpDis=data.frame(cdf=cumsum(table1)/sum(table1), proba=table1/sum(table1), index_scan=min_scan:max_scan)
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EmpDis<-EmpDis[,-2]
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return(EmpDis)
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}
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```
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```{r}
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Plot_CDF <- function(lambda,n_sample,T,tau){
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Emp=EmpDistrib(lambda,n_sample,T,tau)
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title=TeX(paste(r'(Cumulative distribution function for $\lambda=$)', lambda))
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plot(Emp$index_scan, Emp$cdf,type="s",xlab="Number of occurrences",ylab="Probability", main=title, col="red")
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return(Emp)
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}
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```
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```{r}
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n_sample=10**4
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lambda0=3
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T=10
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tau=1
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ppH0=PoissonProcess(lambda0,T)
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#CDF=Plot_CDF(lambda0,n_sample,T,tau)
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```
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```{r}
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PValue <- function(Emp,ppH, T, tau){
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scanH1=ScanStat(ppH,T,tau)[2]
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index_scanH1=ScanStat(ppH,T,tau)[1]
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index=Emp$index_scan
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n=length(index)
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if (scanH1< min(Emp$index_scan)){
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return (c(scanH1,1,index_scanH1))
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} else{
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if(min(Emp$index_scan)<scanH1 && scanH1<=max(Emp$index_scan)){
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return(c(scanH1,1-Emp$cdf[scanH1-min(Emp$index_scan)+1],index_scanH1))
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} else{return (c(scanH1,0,index_scanH1))}}
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}
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```
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```{r}
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NbSeqH0 = 10
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NbSeqH1 = NbSeqH0
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DataH0 = vector("list")
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DataH1 = vector("list")
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lambda0 = 2
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lambda1 = 5
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T = 10
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tau = 1
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#Creation of a sequence that contains the sequence simulated under the null hypothesis
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for (i in 1:NbSeqH0) {
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ppi = PoissonProcess(lambda0,T)
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DataH0[[i]] = ppi
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}
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#Creation of a sequence that contains the sequence simulated under the alternative hypothesis
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seqH1begin = c()
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for (i in 1:NbSeqH1) {
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pphi = SimulationH1(lambda0, lambda1,T,tau)
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DataH1[[i]] = pphi
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}
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#Computation of the time between events
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TimeBetweenEventList <- function(list,n_list){
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TBE = vector("list",length=n_list)
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for (i in (1:n_list)) {
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ppi = list[[i]]
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ni = length(ppi)
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tbei = ppi[2:ni]-ppi[1:ni-1]
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TBE[[i]] = tbei
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}
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return (TBE)
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}
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tbe0 = TimeBetweenEventList(DataH0,NbSeqH0)
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```
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```{r}
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#We start by computing the empirical distribution for lambda0
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Emp = EmpDistrib(lambda0,n_sample,T,tau)
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scan = c()
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pvalue = c()
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index_scan = c()
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#Then, we stock the p-value and the
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for (i in 1:NbSeqH0){
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ppi = DataH0[[i]]
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result = PValue(Emp,ppi,T,tau)
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scan = c(scan,result[1])
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pvalue = c(pvalue,result[2])
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index_scan = c(index_scan,result[3])
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}
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ScS_H0=data.frame(num=(1:NbSeqH0), scan_stat=scan, pvalue_scan=pvalue,class=c(pvalue<0.05)*1)
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head(ScS_H0)
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sum(ScS_H0$class[which(ScS_H0$class=='1')])/NbSeqH0
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```
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```{r}
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#We start by computing the empirical distribution for lambda0
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scan=c()
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pvalue=c()
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index_scan=c()
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#Then, we stock the p-value and the
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for (i in 1:NbSeqH1){
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ppi=DataH1[[i]]
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result=PValue(Emp,DataH1[[i]],T,tau)
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scan=c(scan,result[1])
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pvalue=c(pvalue,result[2])
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index_scan=c(index_scan,result[3])
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}
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ScS_H1 = data.frame(num=1:NbSeqH1, scan_stat=scan, pvalue_scan=pvalue, class=(pvalue<0.05)*1, begin_scan=index_scan)
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head(ScS_H1)
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sum(ScS_H1$class[which(ScS_H1$class=='1')])/NbSeqH1
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```
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```{r}
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ScanStatMC <- function(NbSeq, T, tau, Emp, pp0){
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scan=c()
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pvalue=c()
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index_scan=c()
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for (i in 1:NbSeq){
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ppi=pp0[[i]]
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result=PValue(Emp,ppi,T,tau)
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scan=c(scan,result[1])
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pvalue=c(pvalue,result[2])
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index_scan=c(index_scan,result[3])
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}
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ScS_H0=data.frame(num=(1:NbSeq), scan_stat=scan, pvalue_scan=pvalue,class=c(pvalue<0.05)*1)
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return(ScS_H0)
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}
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```
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```{r}
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ComputeE <- function(lambda0, lambda1){
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E = 1
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maxXk = floor(E*(log(lambda1/lambda0)))
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while (maxXk < 3) {
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E = E+1
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maxXk = floor(E*(log(lambda1/lambda0)))
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}
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return (E)
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}
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```
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```{r}
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ScoreDistribEmpiric <- function(lambda0, lambda1, n_sample, T){
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E = ComputeE(lambda0, lambda1)
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Score = c()
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for (i in 1:n_sample){
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ppH0 = PoissonProcess(lambda0,T)
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n1 = length(ppH0)
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tbe0 = ppH0[2:n1]-ppH0[1:n1-1]
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X = floor(E*(log(lambda1/lambda0)+(lambda0-lambda1)*tbe0))
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Score=c(Score,X)
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}
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min_X = min(Score)
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max_X = max(Score)
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P_X = table(factor(Score, levels = min_X:max_X))/sum(table(Score))
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df = data.frame("Score_X" = min(Score):max(Score), "P_X" = P_X)
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df <- df[,-2]
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return (df)
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}
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```
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```{r}
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ScoreDistribElisa <- function(lambda0, lambda1, T){
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E = ComputeE(lambda0, lambda1)
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score_max = floor(E*log(lambda1/lambda0))
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## score_min compute
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score_min_c = floor(E*log(lambda1/lambda0)+E*(lambda0-lambda1)*T)
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l = seq(score_min_c,score_max,1)
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borne_inf = (l-E*log(lambda1/lambda0))/(E*(lambda0-lambda1))
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borne_sup = (l+1-E*log(lambda1/lambda0))/(E*(lambda0-lambda1))
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proba.l = pexp(rate=lambda0,borne_inf)-pexp(rate=lambda0,borne_sup)
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S = sum(proba.l)
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new.proba.s = proba.l/S
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df = data.frame("Score_X" = l, "P_X" = new.proba.s)
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return (df)
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}
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```
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```{r}
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LocalScoreMC <- function(lambda0, lambda1, NbSeq, T, X_seq, P_X, tbe0){
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E = ComputeE(lambda0, lambda1)
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pvalue = c()
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X = c()
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min_X = min(X_seq)
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max_X = max(X_seq)
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NbSeq.NonNulles = 0
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for (i in 1:NbSeq){
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x = floor(E*log(dexp(tbe0[[i]], rate = lambda1)/dexp(tbe0[[i]], rate = lambda0)))
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if (length(x)!=0){
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X = c(X,x)
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LS = localScoreC(x)$localScore[1]
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daudin_result = daudin(localScore = LS, score_probabilities = P_X, sequence_length = length(x), sequence_min = min_X, sequence_max = max_X)
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options(warn = -1) # Disable warnings print
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pvalue = c(pvalue, daudin_result)
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NbSeq.NonNulles = NbSeq.NonNulles + 1
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}
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}
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LS_H0=data.frame(num=1:NbSeq.NonNulles, pvalue_scan=pvalue, class=(pvalue<0.05)*1)
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return(LS_H0)
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}
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```
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```{r}
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Nb = 10
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tbe0 = vector("list",length = Nb)
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pp0 = vector("list", length = Nb)
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pp1 = vector("list", length = Nb)
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tbe1 = vector("list", length = Nb)
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for (i in (1:Nb)) {
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#Simulation for sequences under H0
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ppi = PoissonProcess(lambda0,T)
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ni=length(ppi)
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pp0[[i]] = ppi
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tbei = ppi[2:ni]-ppi[1:ni-1]
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tbe0[[i]] = tbei
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#Simulation for sequences under H1
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ppj1 = SimulationH1(lambda0, lambda1, T, tau)
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nj = length(ppj1)
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pp1[[i]] = ppj1
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tbej = ppj1[2:nj]-ppj1[1:nj-1]
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tbe1[[i]] = tbej
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}
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Score = ScoreDistribEmpiric(lambda0, lambda1, Nb, T)
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LocalScoreMC(2,3,Nb,10,Score$Score_X, Score$P_X, tbe0)
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LocalScoreMC(2,3,Nb,10,Score$Score_X, Score$P_X, tbe1)
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```
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```{r}
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CompareMethods <- function(lambda0, lambda1, NbSeq, T, tau){
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if (lambda0 < lambda1){
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cat("For T = ", T, ", Nb = ", NbSeq, ", lambda0 = ", lambda0, " and lambda1 = ", lambda1, ":\n", sep = "")
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tbe0 = vector("list",length=NbSeq)
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pp0 = vector("list", length = NbSeq)
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pp1 = vector("list", length = NbSeq)
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tbe1 = vector("list", length = NbSeq)
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for (i in (1:NbSeq)) {
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#Simulation for sequences under H0
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ppi = PoissonProcess(lambda0,T)
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ni=length(ppi)
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pp0[[i]] = ppi
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tbei = ppi[2:ni]-ppi[1:ni-1]
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tbe0[[i]] = tbei
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#Simulation for sequences under H1
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ppj1 = SimulationH1(lambda0, lambda1, T, tau)
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nj = length(ppj1)
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pp1[[i]] = ppj1
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tbej = ppj1[2:nj]-ppj1[1:nj-1]
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tbe1[[i]] = tbej
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}
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#cat("- Empiric version:\n")
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Score = ScoreDistribEmpiric(lambda0, lambda1, NbSeq, T)
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LS_H0 = LocalScoreMC(lambda0, lambda1, NbSeq, T, Score$Score_X, Score$P_X, tbe0)
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LS_H1 = LocalScoreMC(lambda0, lambda1, NbSeq, T, Score$Score_X, Score$P_X, tbe1)
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LS_obtained = c(LS_H0$class, LS_H1$class)
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options(warn = -1)
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Emp = EmpDistrib(lambda0,n_sample,T,tau)
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SS_H0 = ScanStatMC(NbSeq, T, tau, Emp, pp0)
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SS_H1 = ScanStatMC(NbSeq, T, tau, Emp, pp1)
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SS_obtained = c(SS_H0$class, SS_H1$class)
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cat("--- Confusion matrix for scan statistic method --- \n")
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theoretical_results_SS = c(rep(0,length(SS_H0$num)), rep(1,length(SS_H1$num)))
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print(confusionMatrix(as.factor(SS_obtained), as.factor(theoretical_results_SS),
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dnn = c("Prediction", "Reference"))$table)
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cat("--- Confusion matrix for local score method --- \n")
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theoretical_results_LS = c(rep(0,length(LS_H0$num)), rep(1,length(LS_H1$num)))
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print(confusionMatrix(as.factor(LS_obtained), as.factor(theoretical_results_LS),
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dnn = c("Prediction", "Reference"))$table)
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#cat("--- Coube ROC associé")
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title_ROC = TeX(paste(r'(ROC curve for $H_0: \lambda_0=$)', lambda0,
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r'(against $H_1: \lambda_0=$)', lambda1))
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pred.SS = prediction(theoretical_results_SS,SS_obtained)
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pred.LS = prediction(theoretical_results_LS,LS_obtained)
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perf.SS = performance(pred.SS,"tpr", "fpr")
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perf.LS = performance(pred.LS,"tpr", "fpr")
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#plot(perf.SS, lty=1, col="coral")
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par(new=T)
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#plot(perf.LS, lty=2, col="coral", main=title_ROC)
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cat("-----------------------------------\n")
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result <- c('performance.SS'= perf.SS,'performance.LS'= perf.LS)
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return(result)
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}
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}
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```
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```{r}
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NbSeq = 100
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T = 10
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tau = 2
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lambda0 = 0.3
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lambda1 = 0.5
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result1 = CompareMethods(lambda0, lambda1, NbSeq, T, tau)
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lambda0 = 0.01
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lambda1 = 1
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result2 = CompareMethods(lambda0, lambda1, NbSeq, T, tau)
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lambda0 = 1
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lambda1 = 1.1
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result3 = CompareMethods(lambda0, lambda1, NbSeq, T, tau)
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lambda0 = 0.9
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lambda1 = 2
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result4 = CompareMethods(lambda0, lambda1, NbSeq, T, tau)
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title_ROC = TeX(paste(r'(ROC curve for several values of $\lambda_0$ and $\lambda_1$)'))
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perf1SS = result1[1]
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perf1LS = result1[2]
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perf2SS = result2[1]
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perf2LS = result2[2]
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perf3SS = result3[1]
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perf3LS = result3[2]
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perf4SS = result4[1]
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perf4LS = result4[2]
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plot(perf1SS$performance.SS, lty=1, col="coral", lwd = 2)
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par(new=T)
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plot(perf1LS$performance.LS, lty=2, col="coral",lwd = 2)
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par(new=T)
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plot(perf2SS$performance.SS, lty=1, col="cyan4", lwd = 2)
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par(new=T)
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plot(perf2LS$performance.LS, lty=2, col="cyan4", lwd = 2)
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|
||||
par(new=T)
|
||||
plot(perf3SS$performance.SS, lty=1, col="magenta4", lwd = 2)
|
||||
par(new=T)
|
||||
plot(perf3LS$performance.LS, lty=2, col="magenta4", lwd = 2)
|
||||
|
||||
par(new=T)
|
||||
plot(perf4SS$performance.SS, lty=1, col="olivedrab4", lwd = 2)
|
||||
par(new=T)
|
||||
plot(perf4LS$performance.LS, lty=2, col="olivedrab4", lwd = 2,main=title_ROC)
|
||||
|
||||
legend(0.5, 0.3, legend=c("lambda0 = 0.3, lambda1 = 0.5", "lambda0 = 1, lambda1 = 9", "lambda0 = 2, lambda1 = 6", "lambda0 = 8, lambda1 = 9", "lambda0 = 0.1, lambda1 = 0.2")
|
||||
,col=c("coral", "cyan4", "magenta4", "olivedrab4", "lightgoldenrod3"), lty=1, cex=0.9,lwd=4,
|
||||
box.lty=0)
|
||||
```
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
Loading…
x
Reference in New Issue
Block a user