Update of Local score
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Paul-Corbalan
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@ -22,9 +22,12 @@ SimulationH1 <- function(lambda0, lambda1,T,tau){
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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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return (c(ppH1,which(ppH1==min(ppH1.repo))))
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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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@ -93,30 +96,39 @@ 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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n_sample=10**4
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lambda1=4
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T=10
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tau=1
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ppH0=PoissonProcess(lambda1,T)
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CDF=Plot_CDF(lambda1,n_sample,T,tau)
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```
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```{r}
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PValue <- function(Emp,ppH1, T, tau){
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scanH1=ScanStat(ppH1,T,tau)[2]
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index_scanH1=ScanStat(ppH1,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))
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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]))
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} else{return (c(scanH1,0))}}
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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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### 2.2. Simulation under $\mathcal{H}_0$ and computation of p-values
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On simule des séquences sous $\mathcal{H}_0$, que l'on stocke. On calcule la valeur de la scan stat et de la p-value, que l'on stocke aussi. On a une séquence de p-valeur des scans et une séquence de score local.
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```{r}
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NbSeqH0=5
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NbSeqH1=5
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NbSeqH0=5000
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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=3
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lambda1=5
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lambda1=4
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T=10
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tau=1
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@ -127,9 +139,11 @@ for (i in 1:NbSeqH0) {
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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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DataH1[[i]]=pphi[1]
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seqH1begin=c(pphi[2],seqH1begin)
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}
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#Computation of the time between events
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@ -152,6 +166,7 @@ We compute the p-value associated to all 5 sequences, and stock them in a vector
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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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@ -159,12 +174,64 @@ for (i in 1:NbSeqH0){
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result=PValue(Emp,DataH0[[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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cat(paste("\nSimulation for the sequence", i, ", for lambda0=",lambda0, " ,lambda1=", lambda1, " , scan=", result[1] ,"p-value=",result[2]))
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index_scan=c(index_scan,result[3])
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#cat(paste("\nSimulation for the sequence", i, ", for lambda0=",lambda0, " ,lambda1=", lambda1, " , scan=", result[1] ,"p-value=",result[2]))
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#print(length(ppi))
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}
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ScS_H0=data.frame(num=1:NbSeqH0, index=scan, pvalue_scan=pvalue, class=(pvalue<0.05))
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ScS_H0
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ScS_H0=data.frame(num=1:NbSeqH0, scan_stat=scan, pvalue_scan=pvalue, class=(pvalue<0.05), begin_scan=index_scan)
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sum(ScS_H0$class[which(ScS_H0$class==TRUE)])/NbSeqH0
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```
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## 3.Local score
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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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#cat(paste("\nSimulation for the sequence", i, ", for lambda0=",lambda0, " ,lambda1=", lambda1, " , scan=", result[1] ,"p-value=",result[2]))
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#print(length(ppi))
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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), begin_scan=index_scan, begin_seq_H1=seqH1begin)
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sum(ScS_H1$class[which(ScS_H0$class==TRUE)])/NbSeqH1
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ScS_H1
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```
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## 3. Local score
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### Distribution des scores via Monte-Carlo
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```{r}
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# Calcul du choix de E
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E = 1
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maxXk = floor(E*(log(lambda1/lambda0)))
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maxXk
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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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print(E)
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ppH0 = PoissonProcess(lambda0,10^4)
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n1 = length(ppH0)
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tbe0 = ppH0[2:n1]-ppH0[1:n1-1]
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print(ks.test(tbe0,'exp'))
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x = floor(E*(log(lambda1/lambda0)+(lambda0-lambda1)*tbe0)) # ne pas mettre le floor ni le E (certes égale à 1)
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#hist(x)
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#print(summary(x))
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P_X = table(factor(x, levels = min(x):max(x)))
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P_X = P_X/sum(table(x))
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#print(dist.theo.scores) # Mettre à jour avec Elisa
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print(P_X)
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```
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### Calcul du local score
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```{r}
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library("localScore")
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library(Rcpp)
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@ -176,7 +243,7 @@ for (i in 1:NbSeqH0){
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max_X = max(X)
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min_X = min(X)
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P_X = table(factor(X, levels = min_X:max_X))/length(X)
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P_X = table(factor(X, levels = min_X:max_X))/length(X) # supprimer pour les séquences de MC
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LS=localScoreC(X)$localScore[1]
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@ -188,41 +255,3 @@ LS_H0=data.frame(num=1:NbSeqH0, pvalue_scan=pvalue, class=(pvalue<0.05))
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LS_H0
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```
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## A reformater
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```{r}
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# distribtion des scores via MC
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# Nb seq. pp -> Nb seq. tbe -> dist. tbe (vérif) + Nb seq. Scores -> distr scores
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A = 1/(lambda0-lambda1)
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B = A*log(lambda1/lambda0)
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ppH1 = PoissonProcess(lambda1,T)
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n1 = length(ppH1)
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tbe1 = ppH1[2:n1]-ppH1[1:n1-1]
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print(tbe1)
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print(ks.test(tbe1,'exp'))
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x = log(lambda1/lambda0)+(lambda0-lambda1)*tbe1 # ne pas mettre le floor ni le E (certes égale à 1)
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hist(x)
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print(summary(x))
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# Calcul du maximum des scores
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E = 1
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# THEO à faire !!! max.s = log(lambda1/lambda0)
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maxXk = floor(E*(log(lambda1/lambda0)))
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maxXk
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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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print(E)
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x = floor(E*(log(lambda1/lambda0)+(lambda0-lambda1)*tbe1))
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dist.emp.scores = table(x)/sum(table(x))
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dist.emp.scores
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hist(x)
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print(range(x))
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x.verif = seq(range(x)[1],range(x)[2],1)
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dist.theo.scores = lambda0*exp(-lambda0*(A*x.verif-B))
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print(dist.theo.scores)
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print(dist.emp.scores)
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```
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