paul-corbalan/Scan-Statistics-Project-4Y-INSA
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Integration scanstat.Rmd code

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Paul-Corbalan 2022-05-10 10:05:55 +02:00
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commit 799dbef078
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Comparaison_of_methods.rmd
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@ -11,6 +11,7 @@ library("localScore")
library("latex2exp")
library("Rcpp")
library("caret")
library("ROCR")
```
## 1. Proposition for simulations under $\mathcal{H}_1$
@ -370,7 +371,7 @@ LocalScoreMC <- function(lambda0, lambda1, NbSeq, T, X_seq, P_X, tbe0){
pvalue = c(pvalue, daudin_result)
}
LS_H0=data.frame(num=1:NbSeq, pvalue_scan=pvalue, class=(pvalue<0.05))
LS_H0=data.frame(num=1:NbSeq, pvalue_scan=pvalue, class=as.numeric(pvalue<0.05))
return(LS_H0)
}
```
@ -554,3 +555,141 @@ for (i in (1:NbSeq)) {
titleSpec=TeX(paste(r'(Specificity for $\lambda_0=$)', lambda0))
plot(x=accepted_lambda,y=Specificity, type='l', main = titleSpec)
```
## CompareMethods
```{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)
```