---
title: 'Illustration du problème de détection dans le modèle de bruit blanc'
author: "`M2 Statistique, 2017-2018`"
date: "Statistique mathématique en grande dimension et applications, cours de M. Roquain"
output: html_document
runtime: shiny
---




```{r, echo=FALSE}
inputPanel(
  selectInput("m", label = "Number of hypotheses:",
              choices = c(1000 , 10000, 100000), selected = 10000),
  
  sliderInput("s", label = "Sparsity",
              min = 1, max = 1000, value = 5, step = 5), 
 
  sliderInput("delta", label = "Signal strength:",
              min = 0.1, max = 8, value = 3, step = 0.5),
  
  actionButton("takeSample","Sample Now")
 )


rv <- reactiveValues(sample = 0, m = 10000 , s = 5, delta = 3) 

 observeEvent(input$takeSample, {
   rv$sample <-rnorm(as.numeric(input$m))
   rv$m=as.numeric(input$m)
   rv$s=as.numeric(input$s)
   rv$delta=as.numeric(input$delta)
 })
 


renderPlot({
  m= rv$m
  s= rv$s
  delta= rv$delta
  xi=rv$sample
  
  if(input$takeSample){ 
    theta=rep(0,m)
    theta[sample(1:m,s)]=(2*rbinom(s,1,1/2)-1)*delta
    Z=xi+theta
    pvalchi2=pchisq(sum(Z^2),m,lower.tail = FALSE)
    pvalmax=min(2*m*(1-pnorm(max(abs(Z)))),1)
    plot(Z,cex.axis=2,xlab="",ylab="",ylim=c(-7,7),col=gray(0.4),pch=19)  
    lines(1:m,theta,col="lightsalmon",type="s",lwd=3)
    seuil=sqrt(2*log(m))
    abline(h=-seuil,lwd=3,col="lightblue")
    abline(h=+seuil,lwd=3,col="lightblue")
    title(paste("pchi2=",signif(pvalchi2,2),", pmax=",signif(pvalmax,2)),cex.main = 2,col.main= gray(0.2))
  }
},height = 600, width = 1000)
```