Merge branch 'main' of https://github.com/Paul-Corbalan/Scan-Statistics-Project-4Y-INSA
This commit is contained in:
elisaduz
commit
e97a6cb5e8
@ -11,6 +11,8 @@ 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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library("pROC")
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```
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## 1. Proposition for simulations under $\mathcal{H}_1$
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@ -119,17 +121,18 @@ CDF=Plot_CDF(lambda0,n_sample,T,tau)
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Compute $p$-value for scan statistic of `ppH1` with `Emp`:
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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$index_scan
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SS = ScanStat(ppH,T,tau)
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scanH = SS[2]
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index_scanH = SS[1]
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index = Emp$index_scan
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n=length(index)
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if (scanH1< min(Emp$index_scan)){
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return (c(scanH1,1,index_scanH1))
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if (scanH< min(Emp$index_scan)){
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return (c(scanH,1,index_scanH))
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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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if(min(Emp$index_scan)<scanH && scanH<=max(Emp$index_scan)){
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return(c(scanH,1-Emp$cdf[scanH-min(Emp$index_scan)],index_scanH))
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} else{return (c(scanH,0,index_scanH))}}
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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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@ -139,8 +142,9 @@ NbSeqH0=10000
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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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lambda0=1
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lambda1=5
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T=10
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tau=1
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@ -298,9 +302,6 @@ ScoreDistribTheo <- 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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@ -331,10 +332,6 @@ distrib_score_mc = ScoreDistribEmpiric(2,3,10000,T)
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distrib_score_theo = ScoreDistribTheo(2,3,T)
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plot_graph_distrib_score <- function(distrib_score_theo, distrib_score_mc){
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# length(distrib_score_mc[,2])
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# length(distrib_score_theo[,2])
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#diff_distrib_score=abs(distrib_score_mc[,2]-distrib_score_theo[,2])
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#par(mfrow = c(1,2))
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@ -353,204 +350,134 @@ plot_graph_distrib_score(distrib_score_theo, distrib_score_mc)
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### 3.2. Local score calculation
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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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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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LS = localScoreC(x)$localScore[1]
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daudin_result = daudin(localScore = LS, score_probabilities = P_X, sequence_length = length(x), sequence_min = min_X, sequence_max = max_X)
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options(warn = -1) # Disable warnings print
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pvalue = c(pvalue, daudin_result)
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E = ComputeE(lambda0, lambda1)
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pvalue = c()
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X = c()
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min_X = min(X_seq)
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max_X = max(X_seq)
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NbSeq.NonNulles = 0
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for (i in 1:NbSeq){
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x = floor(E*log(dexp(tbe0[[i]], rate = lambda1)/dexp(tbe0[[i]], rate = lambda0)))
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if (length(x)!=0){
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X = c(X,x)
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LS = localScoreC(x)$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, pvalue_scan=pvalue, class=(pvalue<0.05))
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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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## 4. Experience plan for comparaison
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```{r}
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NbSeq = 10**2
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T = 10
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list_of_lambda = list()
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list_of_lambda[[1]] = c(1, 3)
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list_of_lambda[[2]] = c(1, 4)
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list_of_lambda[[3]] = c(1, 5)
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list_of_lambda[[4]] = c(2, 4)
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list_of_lambda[[5]] = c(2, 5)
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list_of_lambda[[6]] = c(2, 6)
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list_of_lambda[[7]] = c(4, 5)
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list_of_lambda[[8]] = c(4, 8)
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list_of_lambda[[9]] = c(4, 10)
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for (Lambda in list_of_lambda){
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lambda0 = Lambda[1]
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lambda1 = Lambda[2]
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Sensitivity = c()
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Specificity = c()
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accepted_lambda = c()
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CompareMethods <- function(lambda0, lambda1, NbSeq, T, tau){
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if (lambda0 < lambda1){
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accepted_lambda = c(accepted_lambda,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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theoretical_results = c(rep(0,NbSeq), rep(1,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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Emp = EmpDistrib(lambda0,n_sample,T,tau)
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X_seq = Score$Score_X
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P_X = Score$P_X
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LS_H0 = LocalScoreMC(lambda0, lambda1, NbSeq, T, X_seq, P_X, tbe0)
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options(warn = -1) # Disable warnings print
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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_expected = c(SS_H0$class, SS_H1$class)
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#cat("Local Score:\n")
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#print(summary(LS_H0))
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#cat("Scan Statistics:\n")
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#print(summary(SS_H0))
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#cat("Confusion Matrix:\n")
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#print(confusionMatrix(factor(LS_H0$class), factor(SS_H0$class)))
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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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#cat("- Elisa version:\n")
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Score = ScoreDistribTheo(lambda0, lambda1, T)
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Emp = EmpDistrib(lambda0,n_sample,T,tau)
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X_seq = Score$Score_X
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P_X = Score$P_X
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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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LS_H0 = LocalScoreMC(lambda0, lambda1, NbSeq, T, X_seq, P_X, tbe0)
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options(warn = -1) # Disable warnings print
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SS_H0 = ScanStatMC(NbSeq, T, tau, Emp, pp0)
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#Simulation for sequences under H1
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ppj1 = SimulationH1(lambda0, lambda1, T, 3)
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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("Local Score:\n")
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#print(summary(LS_H0))
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#cat("Scan Statistics:\n")
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#print(summary(SS_H0))
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#cat("Confusion Matrix:\n")
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print(confusionMatrix(factor(theoretical_results), factor(SS_expected)))
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#Sensitivity = c(Sensitivity,confusionMatrix(factor(theoretical_results), factor(SS_expected))$byClass[1])
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#Specificity = c(Specificity,confusionMatrix(factor(theoretical_results), factor(SS_expected))$byClass[2])
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cat("---\n")
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}
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titleSens=TeX(paste(r'(Sensitivity for $\lambda_0=$)', lambda0))
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plot(x=accepted_lambda,y=Sensitivity, type='l', main = titleSens)
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titleSpec=TeX(paste(r'(Specificity for $\lambda_0=$)', lambda0))
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plot(x=accepted_lambda,y=Specificity, type='l', main = titleSpec)
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#cat("- Empiric version:\n")
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Score = ScoreDistribEmpiric(lambda0, lambda1, 10**5, 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(lambda0,10**5,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"))$table)
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roc_SS = roc(theoretical_results_SS, SS_obtained)
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areaSS = auc(roc_SS)
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cat("Area under the ROC curve for SS = ", areaSS, "\n")
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cat("--- Confusion matrix for local score method --- \n")
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theoretical_results_LS = c(rep(0,length(LS_H0$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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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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par(new=T)
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roc_LS = roc(theoretical_results_LS, LS_obtained)
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areaLS = auc(roc_LS)
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cat("Area under the ROC curve for LS = ", areaLS, "\n")
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cat("-----------------------------------\n")
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options(warn = -1)
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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 = 10**2
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NbSeq = 10**4
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T = 10
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lambda0 = 2
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lambda1 = 5
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n_sample=10**4
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tau = 2
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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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theoretical_results = c(rep(0,NbSeq), rep(1,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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Emp = EmpDistrib(lambda0,n_sample,T,tau)
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list_of_lambda = list()
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list_of_lambda[[1]] = c(1, 3)
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list_of_lambda[[2]] = c(2, 6)
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list_of_lambda[[3]] = c(4, 7)
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list_of_lambda[[4]] = c(2, 9)
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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_expected = c(SS_H0$class, SS_H1$class)
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#cat("Local Score:\n")
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#print(summary(LS_H0))
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#cat("Scan Statistics:\n")
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#print(summary(SS_H0))
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#cat("Confusion Matrix:\n")
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#print(confusionMatrix(factor(LS_H0$class), factor(SS_H0$class)))
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#cat("- Elisa version:\n")
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Score = ScoreDistribTheo(lambda0, lambda1, T)
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Emp = EmpDistrib(lambda0,n_sample,T,tau)
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X_seq = Score$Score_X
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P_X = Score$P_X
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LS_H0 = LocalScoreMC(lambda0, lambda1, NbSeq, T, X_seq, P_X, tbe0)
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options(warn = -1) # Disable warnings print
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i = 1
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legend_list = c()
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SS_H0 = ScanStatMC(NbSeq, T, tau, Emp, pp0)
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#cat("Local Score:\n")
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#print(summary(LS_H0))
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#cat("Scan Statistics:\n")
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#print(summary(SS_H0))
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#cat("Confusion Matrix:\n")
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print(confusionMatrix(factor(theoretical_results), factor(SS_expected)))
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#Sensitivity = c(Sensitivity,confusionMatrix(factor(theoretical_results), factor(SS_expected))$byClass[1])
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#Specificity = c(Specificity,confusionMatrix(factor(theoretical_results), factor(SS_expected))$byClass[2])
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cat("---\n")
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titleSens=TeX(paste(r'(Sensitivity for $\lambda_0=$)', lambda0))
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plot(x=accepted_lambda,y=Sensitivity, type='l', main = titleSens)
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for (Lambda in list_of_lambda){
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lambda0 = Lambda[1]
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lambda1 = Lambda[2]
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result = 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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titleSpec=TeX(paste(r'(Specificity for $\lambda_0=$)', lambda0))
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plot(x=accepted_lambda,y=Specificity, type='l', main = titleSpec)
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perfSS = result[1]
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perfLS = result[2]
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plot(perfSS$performance.SS, lty=1, col=i, lwd = 2)
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par(new=T)
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plot(perfLS$performance.LS, lty=2, col=i,lwd = 2)
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legend_list=c(legend_list, paste(c("lambda0 = ", lambda0, ", lambda1 = ", lambda1), collapse = ""))
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i=i+1
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}
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legend(0.5, 0.3, legend=legend_list, col=1:length(list_of_lambda), lty=1, cex=0.9,lwd=4, box.lty=0)
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```
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478
scanstat.Rmd
478
scanstat.Rmd
@ -1,478 +0,0 @@
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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}
|
||||
SimulationH1 <- function(lambda0, lambda1,T,tau){
|
||||
ppH0=PoissonProcess(lambda0,T)
|
||||
ppH1.segt=PoissonProcess(lambda1,tau)
|
||||
dbt=runif(1,0,T-tau)
|
||||
ppH0bis=PoissonProcess(lambda0,T)
|
||||
ppH1.repo=dbt+ppH1.segt
|
||||
ppH0_avant=ppH0bis[which(ppH0bis<ppH1.repo[1])]
|
||||
ppH0_apres=ppH0bis[which(ppH0bis>ppH1.repo[length(ppH1.repo)])]
|
||||
ppH1=c(ppH0_avant,ppH1.repo,ppH0_apres)
|
||||
return (ppH1)
|
||||
}
|
||||
```
|
||||
|
||||
```{r}
|
||||
TimeBetweenEvent <- function(pp){
|
||||
n=length(pp)
|
||||
tbe=pp[2:n]-pp[1:n1-1]
|
||||
tbe=c(0,tbe)
|
||||
return (tbe)
|
||||
}
|
||||
|
||||
DataFrame <- function(pp,tbe){
|
||||
list=data.frame(ProcessusPoisson=pp, TimeBetweenEvent=tbe)
|
||||
}
|
||||
```
|
||||
|
||||
```{r}
|
||||
ScanStat <- function(pp, T, tau){
|
||||
n=length(pp)
|
||||
stop=n-length(which(pp>(T-tau)))
|
||||
ScanStat=0
|
||||
for (i in (1:stop)) {
|
||||
x=which((pp>=pp[i])&(pp<=(pp[i]+tau)))
|
||||
scan=length(x)
|
||||
if (scan>ScanStat) {ScanStat=scan
|
||||
max=i}
|
||||
}
|
||||
return (c(max,ScanStat))
|
||||
}
|
||||
```
|
||||
|
||||
```{r}
|
||||
EmpDistrib <- function(lambda, n_sample,T,tau){
|
||||
pp=PoissonProcess(lambda,T)
|
||||
scan=c(ScanStat(pp,T, tau)[2])
|
||||
index=c(ScanStat(pp,T, tau)[1])
|
||||
for (i in 2:(n_sample)){
|
||||
pp=PoissonProcess(lambda,T)
|
||||
scan=rbind(scan,ScanStat(pp,T, tau)[2])
|
||||
index=rbind(index,ScanStat(pp,T, tau)[1])
|
||||
}
|
||||
min_scan=min(scan)-1
|
||||
max_scan=max(scan)
|
||||
table1=table(factor(scan, levels = min_scan:max_scan))
|
||||
EmpDis=data.frame(cdf=cumsum(table1)/sum(table1), proba=table1/sum(table1), index_scan=min_scan:max_scan)
|
||||
EmpDis<-EmpDis[,-2]
|
||||
return(EmpDis)
|
||||
}
|
||||
```
|
||||
|
||||
|
||||
```{r}
|
||||
Plot_CDF <- function(lambda,n_sample,T,tau){
|
||||
Emp=EmpDistrib(lambda,n_sample,T,tau)
|
||||
title=TeX(paste(r'(Cumulative distribution function for $\lambda=$)', lambda))
|
||||
plot(Emp$index_scan, Emp$cdf,type="s",xlab="Number of occurrences",ylab="Probability", main=title, col="red")
|
||||
return(Emp)
|
||||
}
|
||||
```
|
||||
|
||||
```{r}
|
||||
n_sample=10**4
|
||||
lambda0=3
|
||||
T=10
|
||||
tau=1
|
||||
ppH0=PoissonProcess(lambda0,T)
|
||||
#CDF=Plot_CDF(lambda0,n_sample,T,tau)
|
||||
```
|
||||
|
||||
```{r}
|
||||
PValue <- function(Emp,ppH, T, tau){
|
||||
scanH1=ScanStat(ppH,T,tau)[2]
|
||||
index_scanH1=ScanStat(ppH,T,tau)[1]
|
||||
index=Emp$index_scan
|
||||
n=length(index)
|
||||
if (scanH1< min(Emp$index_scan)){
|
||||
return (c(scanH1,1,index_scanH1))
|
||||
} else{
|
||||
if(min(Emp$index_scan)<scanH1 && scanH1<=max(Emp$index_scan)){
|
||||
return(c(scanH1,1-Emp$cdf[scanH1-min(Emp$index_scan)+1],index_scanH1))
|
||||
} else{return (c(scanH1,0,index_scanH1))}}
|
||||
}
|
||||
```
|
||||
|
||||
```{r}
|
||||
NbSeqH0 = 10
|
||||
NbSeqH1 = NbSeqH0
|
||||
DataH0 = vector("list")
|
||||
DataH1 = vector("list")
|
||||
lambda0 = 2
|
||||
lambda1 = 5
|
||||
T = 10
|
||||
tau = 1
|
||||
|
||||
#Creation of a sequence that contains the sequence simulated under the null hypothesis
|
||||
for (i in 1:NbSeqH0) {
|
||||
ppi = PoissonProcess(lambda0,T)
|
||||
DataH0[[i]] = ppi
|
||||
}
|
||||
|
||||
#Creation of a sequence that contains the sequence simulated under the alternative hypothesis
|
||||
seqH1begin = c()
|
||||
for (i in 1:NbSeqH1) {
|
||||
pphi = SimulationH1(lambda0, lambda1,T,tau)
|
||||
DataH1[[i]] = pphi
|
||||
}
|
||||
|
||||
#Computation of the time between events
|
||||
TimeBetweenEventList <- function(list,n_list){
|
||||
TBE = vector("list",length=n_list)
|
||||
for (i in (1:n_list)) {
|
||||
ppi = list[[i]]
|
||||
ni = length(ppi)
|
||||
tbei = ppi[2:ni]-ppi[1:ni-1]
|
||||
TBE[[i]] = tbei
|
||||
}
|
||||
return (TBE)
|
||||
}
|
||||
tbe0 = TimeBetweenEventList(DataH0,NbSeqH0)
|
||||
```
|
||||
|
||||
```{r}
|
||||
#We start by computing the empirical distribution for lambda0
|
||||
Emp = EmpDistrib(lambda0,n_sample,T,tau)
|
||||
scan = c()
|
||||
pvalue = c()
|
||||
index_scan = c()
|
||||
|
||||
#Then, we stock the p-value and the
|
||||
for (i in 1:NbSeqH0){
|
||||
ppi = DataH0[[i]]
|
||||
result = PValue(Emp,ppi,T,tau)
|
||||
scan = c(scan,result[1])
|
||||
pvalue = c(pvalue,result[2])
|
||||
index_scan = c(index_scan,result[3])
|
||||
}
|
||||
|
||||
ScS_H0=data.frame(num=(1:NbSeqH0), scan_stat=scan, pvalue_scan=pvalue,class=c(pvalue<0.05)*1)
|
||||
head(ScS_H0)
|
||||
sum(ScS_H0$class[which(ScS_H0$class=='1')])/NbSeqH0
|
||||
```
|
||||
|
||||
```{r}
|
||||
#We start by computing the empirical distribution for lambda0
|
||||
scan=c()
|
||||
pvalue=c()
|
||||
index_scan=c()
|
||||
|
||||
#Then, we stock the p-value and the
|
||||
for (i in 1:NbSeqH1){
|
||||
ppi=DataH1[[i]]
|
||||
result=PValue(Emp,DataH1[[i]],T,tau)
|
||||
scan=c(scan,result[1])
|
||||
pvalue=c(pvalue,result[2])
|
||||
index_scan=c(index_scan,result[3])
|
||||
}
|
||||
ScS_H1 = data.frame(num=1:NbSeqH1, scan_stat=scan, pvalue_scan=pvalue, class=(pvalue<0.05)*1, begin_scan=index_scan)
|
||||
head(ScS_H1)
|
||||
sum(ScS_H1$class[which(ScS_H1$class=='1')])/NbSeqH1
|
||||
```
|
||||
|
||||
```{r}
|
||||
ScanStatMC <- function(NbSeq, T, tau, Emp, pp0){
|
||||
scan=c()
|
||||
pvalue=c()
|
||||
index_scan=c()
|
||||
|
||||
for (i in 1:NbSeq){
|
||||
ppi=pp0[[i]]
|
||||
result=PValue(Emp,ppi,T,tau)
|
||||
scan=c(scan,result[1])
|
||||
pvalue=c(pvalue,result[2])
|
||||
index_scan=c(index_scan,result[3])
|
||||
}
|
||||
|
||||
ScS_H0=data.frame(num=(1:NbSeq), scan_stat=scan, pvalue_scan=pvalue,class=c(pvalue<0.05)*1)
|
||||
return(ScS_H0)
|
||||
}
|
||||
```
|
||||
|
||||
```{r}
|
||||
ComputeE <- function(lambda0, lambda1){
|
||||
E = 1
|
||||
maxXk = floor(E*(log(lambda1/lambda0)))
|
||||
while (maxXk < 3) {
|
||||
E = E+1
|
||||
maxXk = floor(E*(log(lambda1/lambda0)))
|
||||
}
|
||||
|
||||
return (E)
|
||||
}
|
||||
```
|
||||
|
||||
```{r}
|
||||
ScoreDistribEmpiric <- function(lambda0, lambda1, n_sample, T){
|
||||
E = ComputeE(lambda0, lambda1)
|
||||
Score = c()
|
||||
|
||||
for (i in 1:n_sample){
|
||||
ppH0 = PoissonProcess(lambda0,T)
|
||||
n1 = length(ppH0)
|
||||
tbe0 = ppH0[2:n1]-ppH0[1:n1-1]
|
||||
X = floor(E*(log(lambda1/lambda0)+(lambda0-lambda1)*tbe0))
|
||||
Score=c(Score,X)
|
||||
}
|
||||
min_X = min(Score)
|
||||
max_X = max(Score)
|
||||
|
||||
P_X = table(factor(Score, levels = min_X:max_X))/sum(table(Score))
|
||||
df = data.frame("Score_X" = min(Score):max(Score), "P_X" = P_X)
|
||||
df <- df[,-2]
|
||||
|
||||
return (df)
|
||||
}
|
||||
```
|
||||
|
||||
```{r}
|
||||
ScoreDistribElisa <- function(lambda0, lambda1, T){
|
||||
E = ComputeE(lambda0, lambda1)
|
||||
|
||||
score_max = floor(E*log(lambda1/lambda0))
|
||||
|
||||
## score_min compute
|
||||
score_min_c = floor(E*log(lambda1/lambda0)+E*(lambda0-lambda1)*T)
|
||||
|
||||
l = seq(score_min_c,score_max,1)
|
||||
borne_inf = (l-E*log(lambda1/lambda0))/(E*(lambda0-lambda1))
|
||||
borne_sup = (l+1-E*log(lambda1/lambda0))/(E*(lambda0-lambda1))
|
||||
proba.l = pexp(rate=lambda0,borne_inf)-pexp(rate=lambda0,borne_sup)
|
||||
S = sum(proba.l)
|
||||
new.proba.s = proba.l/S
|
||||
df = data.frame("Score_X" = l, "P_X" = new.proba.s)
|
||||
|
||||
return (df)
|
||||
}
|
||||
```
|
||||
|
||||
```{r}
|
||||
LocalScoreMC <- function(lambda0, lambda1, NbSeq, T, X_seq, P_X, tbe0){
|
||||
E = ComputeE(lambda0, lambda1)
|
||||
pvalue = c()
|
||||
X = c()
|
||||
min_X = min(X_seq)
|
||||
max_X = max(X_seq)
|
||||
NbSeq.NonNulles = 0
|
||||
for (i in 1:NbSeq){
|
||||
x = floor(E*log(dexp(tbe0[[i]], rate = lambda1)/dexp(tbe0[[i]], rate = lambda0)))
|
||||
if (length(x)!=0){
|
||||
X = c(X,x)
|
||||
LS = localScoreC(x)$localScore[1]
|
||||
daudin_result = daudin(localScore = LS, score_probabilities = P_X, sequence_length = length(x), sequence_min = min_X, sequence_max = max_X)
|
||||
options(warn = -1) # Disable warnings print
|
||||
pvalue = c(pvalue, daudin_result)
|
||||
NbSeq.NonNulles = NbSeq.NonNulles + 1
|
||||
|
||||
}
|
||||
}
|
||||
LS_H0=data.frame(num=1:NbSeq.NonNulles, pvalue_scan=pvalue, class=(pvalue<0.05)*1)
|
||||
return(LS_H0)
|
||||
}
|
||||
```
|
||||
|
||||
```{r}
|
||||
Nb = 10
|
||||
tbe0 = vector("list",length = Nb)
|
||||
pp0 = vector("list", length = Nb)
|
||||
pp1 = vector("list", length = Nb)
|
||||
tbe1 = vector("list", length = Nb)
|
||||
|
||||
for (i in (1:Nb)) {
|
||||
#Simulation for sequences under H0
|
||||
ppi = PoissonProcess(lambda0,T)
|
||||
ni=length(ppi)
|
||||
pp0[[i]] = ppi
|
||||
tbei = ppi[2:ni]-ppi[1:ni-1]
|
||||
tbe0[[i]] = tbei
|
||||
|
||||
#Simulation for sequences under H1
|
||||
ppj1 = SimulationH1(lambda0, lambda1, T, tau)
|
||||
nj = length(ppj1)
|
||||
pp1[[i]] = ppj1
|
||||
tbej = ppj1[2:nj]-ppj1[1:nj-1]
|
||||
tbe1[[i]] = tbej
|
||||
}
|
||||
|
||||
Score = ScoreDistribEmpiric(lambda0, lambda1, Nb, T)
|
||||
LocalScoreMC(2,3,Nb,10,Score$Score_X, Score$P_X, tbe0)
|
||||
LocalScoreMC(2,3,Nb,10,Score$Score_X, Score$P_X, tbe1)
|
||||
```
|
||||
|
||||
```{r}
|
||||
CompareMethods <- function(lambda0, lambda1, NbSeq, T, tau){
|
||||
if (lambda0 < lambda1){
|
||||
|
||||
cat("For T = ", T, ", Nb = ", NbSeq, ", lambda0 = ", lambda0, " and lambda1 = ", lambda1, ":\n", sep = "")
|
||||
tbe0 = vector("list",length=NbSeq)
|
||||
pp0 = vector("list", length = NbSeq)
|
||||
pp1 = vector("list", length = NbSeq)
|
||||
tbe1 = vector("list", length = NbSeq)
|
||||
|
||||
for (i in (1:NbSeq)) {
|
||||
#Simulation for sequences under H0
|
||||
ppi = PoissonProcess(lambda0,T)
|
||||
ni=length(ppi)
|
||||
pp0[[i]] = ppi
|
||||
tbei = ppi[2:ni]-ppi[1:ni-1]
|
||||
tbe0[[i]] = tbei
|
||||
|
||||
#Simulation for sequences under H1
|
||||
ppj1 = SimulationH1(lambda0, lambda1, T, tau)
|
||||
nj = length(ppj1)
|
||||
pp1[[i]] = ppj1
|
||||
tbej = ppj1[2:nj]-ppj1[1:nj-1]
|
||||
tbe1[[i]] = tbej
|
||||
}
|
||||
|
||||
#cat("- Empiric version:\n")
|
||||
Score = ScoreDistribEmpiric(lambda0, lambda1, NbSeq, T)
|
||||
LS_H0 = LocalScoreMC(lambda0, lambda1, NbSeq, T, Score$Score_X, Score$P_X, tbe0)
|
||||
LS_H1 = LocalScoreMC(lambda0, lambda1, NbSeq, T, Score$Score_X, Score$P_X, tbe1)
|
||||
LS_obtained = c(LS_H0$class, LS_H1$class)
|
||||
options(warn = -1)
|
||||
|
||||
Emp = EmpDistrib(lambda0,n_sample,T,tau)
|
||||
SS_H0 = ScanStatMC(NbSeq, T, tau, Emp, pp0)
|
||||
SS_H1 = ScanStatMC(NbSeq, T, tau, Emp, pp1)
|
||||
SS_obtained = c(SS_H0$class, SS_H1$class)
|
||||
|
||||
|
||||
cat("--- Confusion matrix for scan statistic method --- \n")
|
||||
theoretical_results_SS = c(rep(0,length(SS_H0$num)), rep(1,length(SS_H1$num)))
|
||||
print(confusionMatrix(as.factor(SS_obtained), as.factor(theoretical_results_SS),
|
||||
dnn = c("Prediction", "Reference"))$table)
|
||||
|
||||
cat("--- Confusion matrix for local score method --- \n")
|
||||
theoretical_results_LS = c(rep(0,length(LS_H0$num)), rep(1,length(LS_H1$num)))
|
||||
print(confusionMatrix(as.factor(LS_obtained), as.factor(theoretical_results_LS),
|
||||
dnn = c("Prediction", "Reference"))$table)
|
||||
|
||||
#cat("--- Coube ROC associé")
|
||||
title_ROC = TeX(paste(r'(ROC curve for $H_0: \lambda_0=$)', lambda0,
|
||||
r'(against $H_1: \lambda_0=$)', lambda1))
|
||||
pred.SS = prediction(theoretical_results_SS,SS_obtained)
|
||||
pred.LS = prediction(theoretical_results_LS,LS_obtained)
|
||||
perf.SS = performance(pred.SS,"tpr", "fpr")
|
||||
perf.LS = performance(pred.LS,"tpr", "fpr")
|
||||
#plot(perf.SS, lty=1, col="coral")
|
||||
par(new=T)
|
||||
#plot(perf.LS, lty=2, col="coral", main=title_ROC)
|
||||
cat("-----------------------------------\n")
|
||||
|
||||
|
||||
result <- c('performance.SS'= perf.SS,'performance.LS'= perf.LS)
|
||||
return(result)
|
||||
}
|
||||
}
|
||||
```
|
||||
|
||||
```{r}
|
||||
NbSeq = 100
|
||||
T = 10
|
||||
tau = 2
|
||||
lambda0 = 0.3
|
||||
lambda1 = 0.5
|
||||
|
||||
result1 = CompareMethods(lambda0, lambda1, NbSeq, T, tau)
|
||||
|
||||
lambda0 = 0.01
|
||||
lambda1 = 1
|
||||
|
||||
result2 = CompareMethods(lambda0, lambda1, NbSeq, T, tau)
|
||||
|
||||
lambda0 = 1
|
||||
lambda1 = 1.1
|
||||
|
||||
result3 = CompareMethods(lambda0, lambda1, NbSeq, T, tau)
|
||||
|
||||
|
||||
lambda0 = 0.9
|
||||
lambda1 = 2
|
||||
|
||||
result4 = CompareMethods(lambda0, lambda1, NbSeq, T, tau)
|
||||
|
||||
|
||||
title_ROC = TeX(paste(r'(ROC curve for several values of $\lambda_0$ and $\lambda_1$)'))
|
||||
|
||||
perf1SS = result1[1]
|
||||
perf1LS = result1[2]
|
||||
|
||||
perf2SS = result2[1]
|
||||
perf2LS = result2[2]
|
||||
|
||||
perf3SS = result3[1]
|
||||
perf3LS = result3[2]
|
||||
|
||||
perf4SS = result4[1]
|
||||
perf4LS = result4[2]
|
||||
|
||||
|
||||
plot(perf1SS$performance.SS, lty=1, col="coral", lwd = 2)
|
||||
par(new=T)
|
||||
plot(perf1LS$performance.LS, lty=2, col="coral",lwd = 2)
|
||||
|
||||
par(new=T)
|
||||
plot(perf2SS$performance.SS, lty=1, col="cyan4", lwd = 2)
|
||||
par(new=T)
|
||||
plot(perf2LS$performance.LS, lty=2, col="cyan4", lwd = 2)
|
||||
|
||||
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)
|
||||
```
|
||||
|
||||
|
||||
|
||||
|
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Reference in New Issue
Block a user