Import from https://github.com/armandfavrot/mysubmission

.Rprofile

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+source("renv/activate.R")

.gitignore

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+.Rproj.user
+.Rhistory
+.RData
+.Ruserdata
+
+_extensions
+renv
+/.quarto/

_quarto.yml

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+project:
+  type: website
+  title: "submitted-202310-favrot-pest"
+
+

functions/gelman.R

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+
+
+
+# Functions of gelman.R, in the coda package. Ref : https://rdrr.io/cran/coda/src/R/gelman.R 
+# Functions to recode gelman.plot with ggplot2 (cf /functions/gelman.plot2.R)
+
+
+"gelman.diag" <- function (x, confidence = 0.95, transform = FALSE,
+                           autoburnin=TRUE, multivariate=TRUE) 
+  ## Gelman and Rubin's diagnostic
+  ## Gelman, A. and Rubin, D (1992). Inference from iterative simulation
+  ## using multiple sequences.  Statistical Science, 7, 457-551.
+  ##
+  ## Correction and Multivariate generalization:
+  ## Brooks, S.P. and Gelman, A. (1997) General methods for monitoring
+  ## convergence of iterative simulations. Journal of Computational and
+  ## Graphical Statistics, 7, 434-455.
+
+{
+  x <- as.mcmc.list(x)
+  if (nchain(x) < 2) 
+    stop("You need at least two chains")
+  ## RGA added an autoburnin parameter here, because if I have already
+  ## trimmed burn in, I don't want to do it again.
+  if (autoburnin && start(x) < end(x)/2 ) 
+    x <- window(x, start = end(x)/2 + 1)
+  Niter <- niter(x)
+  Nchain <- nchain(x)
+  Nvar <- nvar(x)
+  xnames <- varnames(x)
+
+  if(transform)
+    x <- gelman.transform(x)
+  ##
+  ## Estimate mean within-chain variance (W) and between-chain variance
+  ## (B/Niter), and calculate sampling variances and covariance of the
+  ## estimates (varW, varB, covWB)
+  ##
+  ## Multivariate (upper case)
+  x <- lapply(x, as.matrix)
+  S2 <- array(sapply(x, var, simplify=TRUE), dim=c(Nvar,Nvar,Nchain))
+  W <- apply(S2, c(1,2), mean)
+  xbar <- matrix(sapply(x, apply, 2, mean, simplify=TRUE), nrow=Nvar,
+                 ncol=Nchain)
+  B <- Niter * var(t(xbar))
+
+  if(Nvar > 1 && multivariate) {
+    ## We want the maximal eigenvalue of the square matrix X that
+    ## solves WX = B. It is numerically easier to work with a
+    ## symmetric matrix that has the same eigenvalues as X.
+    if (is.R()) {
+      CW <- chol(W)
+      emax <- eigen(backsolve(CW, t(backsolve(CW, B, transpose=TRUE)),
+                              transpose=TRUE),
+                    symmetric=TRUE, only.values=TRUE)$values[1]
+    }
+    else {
+      emax <- eigen(qr.solve(W,B), symmetric=FALSE, only.values=TRUE)$values
+    }
+    mpsrf <- sqrt( (1 - 1/Niter) + (1 + 1/Nvar) * emax/Niter )
+  }
+  else
+    mpsrf <- NULL
+  ## Univariate (lower case)
+  w <- diag(W)
+  b <- diag(B)
+
+
+  s2 <- matrix(apply(S2, 3, diag), nrow=Nvar, ncol=Nchain)
+  muhat <- apply(xbar,1,mean)
+  var.w <- apply(s2, 1, var)/Nchain              
+  var.b <- (2 * b^2)/(Nchain - 1)      
+  cov.wb <- (Niter/Nchain) * diag(var(t(s2), t(xbar^2)) -
+                                    2 * muhat * var(t(s2), t(xbar)))
+  ##
+  ## Posterior interval combines all uncertainties in a t interval with
+  ## center muhat, scale sqrt(V), and df.V degrees of freedom.
+  ##
+  V <- (Niter - 1) * w / Niter  + (1 + 1/Nchain) * b/ Niter
+  var.V <- ((Niter - 1)^2 * var.w + (1 + 1/Nchain)^2 * 
+              var.b + 2 * (Niter - 1) * (1 + 1/Nchain) * cov.wb)/Niter^2
+  df.V <- (2 * V^2)/var.V
+  ##
+  ## Potential scale reduction factor (that would be achieved by
+  ## continuing simulations forever) is estimated by 
+  ##   R = sqrt(V/W) * df.adj
+  ## where df.adj is a degrees of freedom adjustment for the width
+  ## of the t-interval.
+  ##
+  ## To calculate upper confidence interval we divide R2 = R^2 into two
+  ## parts, fixed and random.  The upper limit of the random part is
+  ## calculated assuming that B/W has an F distribution.
+  ##
+  df.adj <- (df.V + 3)/(df.V + 1)
+  B.df <- Nchain - 1
+  W.df <- (2 * w^2)/var.w
+  R2.fixed <- (Niter - 1)/Niter
+  R2.random <- (1 + 1/Nchain) * (1/Niter) * (b/w)
+  R2.estimate <- R2.fixed + R2.random
+  R2.upper <- R2.fixed + qf((1 + confidence)/2, B.df, W.df) * R2.random
+  psrf <- cbind(sqrt(df.adj * R2.estimate), sqrt(df.adj * R2.upper))
+  dimnames(psrf) <- list(xnames, c("Point est.", "Upper C.I."))
+
+  out <- list(psrf = psrf, mpsrf=mpsrf)
+  class(out) <- "gelman.diag"
+  out
+}
+
+"gelman.transform" <- function(x)
+  ## Gelman and Rubin diagnostic assumes a normal distribution. To
+  ## improve the normal approximation, variables on [0, Inf) are log
+  ## transformed, and variables on [0,1] are logit-transformed.
+{
+  if (!is.R())  {
+    # in S-PLUS this function generates a superfluous warning,
+    # so turn off all warnings during the function.
+    oldWarn <- getOption("warn")
+    options(warn=-1)
+    on.exit(options (warn=oldWarn))
+  }
+  if (nvar(x) == 1) {
+    z <- data.frame(lapply(x, unclass))
+    if (min(z) > 0) {
+      y <- if(max(z) < 1)
+        log(z/(1-z))
+      else log(z)
+      for (j in 1:nchain(x)) x[[j]] <- y[,j]
+    }
+  }
+  else for (i in 1:nvar(x)) {
+    z <- data.frame(lapply(x[, i], unclass))
+    if (min(z) > 0) {
+      y <- if (max(z) < 1) 
+        log(z/(1 - z))
+      else log(z)
+      for (j in 1:nchain(x)) x[[j]][, i] <- y[, j]
+    }
+  }
+  return(x)
+}
+
+"gelman.mv.diag" <- function (x, confidence = 0.95, transform = FALSE)
+{
+  s2 <- sapply(x, var, simplify=TRUE)
+  W <- matrix(apply(s2, 1, mean), nvar(x), nvar(x))
+  xbar <- sapply(x, apply, 2, mean, simplify=TRUE)
+  B <- niter(x) * var(t(xbar))
+  emax <- eigen(qr.solve(W,B), symmetric=FALSE, only.values=TRUE)$values[1]
+  mpsrf <- sqrt( (1 - 1/niter(x)) + (1 + 1/nvar(x)) * emax )
+  return(mpsrf)
+}
+
+
+"print.gelman.diag" <-
+  function (x, digits = 3, ...) 
+  {
+    cat("Potential scale reduction factors:\n\n")
+    print.default(x$psrf, digits = digits, ...)
+    if(!is.null(x$mpsrf)) {
+      cat("\nMultivariate psrf\n\n")
+      cat(format(x$mpsrf,digits = digits))
+    }
+    cat("\n")
+  }
+
+"gelman.plot" <-
+  function (x, bin.width = 10, max.bins = 50, confidence = 0.95,
+            transform = FALSE, autoburnin = TRUE, auto.layout = TRUE, ask,
+            col = 1:2, lty = 1:2, xlab = "last iteration in chain",
+            ylab = "shrink factor", type = "l", ...) 
+  {
+    if (missing(ask)) {
+      ask <- if (is.R()) {
+        dev.interactive()
+      }
+      else {
+        interactive()
+      }
+    }
+    x <- as.mcmc.list(x)
+    oldpar <- NULL
+    on.exit(par(oldpar))
+    if (auto.layout) 
+      oldpar <- par(mfrow = set.mfrow(Nchains = nchain(x), Nparms = nvar(x)))
+    y <- gelman.preplot(x, bin.width = bin.width, max.bins = max.bins, 
+                        confidence = confidence, transform = transform,
+                        autoburnin = autoburnin)
+    all.na <- apply(is.na(y$shrink[, , 1, drop = FALSE]), 2, all)
+    if (!any(all.na)) 
+      for (j in 1:nvar(x)) {
+        matplot(y$last.iter, y$shrink[, j, ], col = col, 
+                lty = lty, xlab = xlab, ylab = ylab, type = type, 
+                ...)
+        abline(h = 1)
+        ymax <- max(c(1, y$shrink[, j, ]), na.rm = TRUE)
+        leg <- dimnames(y$shrink)[[3]]
+        xmax <- max(y$last.iter)
+        legend(xmax, ymax, legend = leg, lty = lty, bty = "n", 
+               col = col, xjust = 1, yjust = 1)
+        title(main = varnames(x)[j])
+        if (j==1)
+          oldpar <- c(oldpar, par(ask = ask))
+      }
+    return(invisible(y))
+  }
+
+"gelman.preplot" <-
+  function (x, bin.width = bin.width, max.bins = max.bins,
+            confidence = confidence, transform = transform,
+            autoburnin = autoburnin) 
+  {
+    x <- as.mcmc.list(x)
+    nbin <- min(floor((niter(x) - 50)/thin(x)), max.bins)
+    if (nbin < 1) {
+      stop("Insufficient iterations to produce Gelman-Rubin plot")
+    }
+    binw <- floor((niter(x) - 50)/nbin)
+    last.iter <- c(seq(from = start(x) + 50 * thin(x), by = binw * 
+                         thin(x), length = nbin), end(x))
+    shrink <- array(dim = c(nbin + 1, nvar(x), 2))
+    dimnames(shrink) <- list(last.iter, varnames(x),
+                             c("median", paste(50 * (confidence + 1), "%",
+                                               sep = ""))
+    )
+    for (i in 1:(nbin + 1)) {
+      shrink[i, , ] <- gelman.diag(window(x, end = last.iter[i]), 
+                                   confidence = confidence,
+                                   transform = transform,
+                                   autoburnin = autoburnin,
+                                   multivariate = FALSE)$psrf
+    }
+    all.na <- apply(is.na(shrink[, , 1, drop = FALSE]), 2, all)
+    if (any(all.na)) {
+      cat("\n******* Error: *******\n")
+      cat("Cannot compute Gelman & Rubin's diagnostic for any chain \n")
+      cat("segments for variables", varnames(x)[all.na], "\n")
+      cat("This indicates convergence failure\n")
+    }
+    return(list(shrink = shrink, last.iter = last.iter))
+  }
+
+if (!is.R()){
+
+  qr.solve <- function (a, b, tol = 1e-07) {
+    if (!is.qr(a))
+      a <- qr(a, tol = tol)
+    nc <- ncol(a$qr)
+    if (a$rank != nc)
+      stop("singular matrix 'a' in solve")
+    if (missing(b)) {
+      if (nc != nrow(a$qr))
+        stop("only square matrices can be inverted")
+      b <- diag(1, nc)
+    }
+    return(qr.coef(a, b))
+  }
+
+}

functions/gelman.plot2.R

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+
+source(file = "functions/gelman.R")
+
+# function adapted from gelman.plot, using ggplot instead of plot
+
+gelman.plot2 <- function (x, coef, bin.width = 10, max.bins = 50, confidence = 0.95, 
+                          transform = FALSE, autoburnin = TRUE, auto.layout = TRUE, 
+                          ask, col = 1:2, lty = 1:2, xlab = "last iteration in chain", 
+                          ylab = "shrink factor", type = "l", ncol = 4, ...){
+  exclude = which((summary(x)$statistics %>% rownames) %in% c("gamma0[1]", "gamma1[1]"))
+  x = x[, - exclude]
+  if (missing(ask)) {
+    ask <- if (is.R()) {
+      dev.interactive()
+    }
+    else {
+      interactive()
+    }
+  }
+  x <- as.mcmc.list(x)
+  oldpar <- NULL
+  on.exit(par(oldpar))
+
+  y <- gelman.preplot(x, bin.width = bin.width, max.bins = max.bins, 
+                      confidence = confidence, transform = transform, autoburnin = autoburnin)
+  all.na <- apply(is.na(y$shrink[, , 1, drop = FALSE]), 2, 
+                  all)
+  l = list()
+  df_value = data.frame(median = NULL, bsup = NULL, Param = NULL, iter = NULL)
+  coef = rownames(summary(x)$statistics)
+  if (!any(all.na)){ 
+    for (j in 1:nvar(x)) {
+      df_temp = as.data.frame(y$shrink[, j, ]);   df_temp$Param = coef[j];    df_temp$iter = y$last.iter;   colnames(df_temp)[c(1, 2)] = c("median", "97.5%")
+      df_value = rbind(df_value, df_temp)
+    }
+  }    
+
+  df_res = df_value %>% pivot_longer(cols = c(median, `97.5%`)) %>% as.data.frame %>% 
+    mutate(Param = recode(Param, "alpha0" = "c100", "alpha1" = "c101", "gamma0[2]" = "c102",
+                          "gamma0[3]" = "c104", "gamma0[4]" = "c105", "gamma1[2]" = "c106",
+                          "gamma1[3]" = "c107", "gamma1[4]" = "c108", "sigma0" = "c109", "chi" = "c110", "eta" = "c111",
+                          "Eff[2,1]" = "c112", "Eff[3,1]" = "c113", "Eff[4,1]" = "c114", 
+                          "Eff[2,2]" = "c115", "Eff[3,2]" = "c116", "Eff[4,2]" = "c117"))
+
+  titre1 = TeX("$\\alpha_0$");   titre2 = TeX("$\\alpha_1$");   
+
+  titre3 = TeX("$\\gamma_0 - Mavrik Jet$");   titre4 = TeX("$\\gamma_0 - Movento$");   titre5 = TeX("$\\gamma_0 - Teppeki$");   
+  titre6 = TeX("$\\gamma_1 - Mavrik Jet$");   titre7 = TeX("$\\gamma_1 - Movento$");   titre8 = TeX("$\\gamma_1 - Teppeki$");   
+
+  titre9 = TeX("$\\sigma_0$");   titre10 = TeX("$\\chi$");   titre11 = TeX("$\\eta$");   
+
+  titre12 = TeX("$Ef_6 - Mavrik Jet$");   titre13 = TeX("$Ef_6 - Movento$");    titre14 = TeX("$Ef_6 - Teppeki$")
+  titre15 = TeX("$Ef_{12} - Mavrik Jet$");   titre16 = TeX("$Ef_{12} - Movento$");    titre17 = TeX("$Ef_{12} - Teppeki$")
+
+  df_res = df_res %>% mutate(Param = as.factor(Param))
+
+  levels(df_res$Param) = c(titre1, titre2, titre3, titre4, titre5, titre6, titre7, titre8, titre9, titre10, titre11,
+                           titre12, titre13, titre14, titre15, titre16, titre17)
+
+  return(ggplot(df_res) + geom_line(aes(x = iter, y = value, color = name, linetype = name)) + facet_wrap(~ Param, ncol = ncol, labeller = label_parsed) +
+           xlab("Last iteration in chain") + ylab("Shrink factor") + theme(legend.position = "bottom") + theme(legend.title = element_blank()) +
+           scale_linetype_manual(values = c("dotted", "solid")) + 
+           scale_color_manual(values = c("red", "black")))
+}

functions/plot_chains.R

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+
+# function to plot the MCMC algorithm's chains obtained from the inference on real data
+
+plot_chains <- function(samp, nrow = 3){
+
+  n = dim(samp[[1]])[1]
+  p = dim(samp[[1]])[2]
+
+  df_temp = rbind(samp[[1]] %>% as.data.frame %>% mutate(i = c(1 : n), chaine = "1"),
+                  samp[[2]] %>% as.data.frame %>% mutate(i = c(1 : n), chaine = "2")) %>% select(- `gamma0[1]`, - `gamma1[1]`)
+
+  df_plot = df_temp %>% pivot_longer(cols = c(1 : (p - 2))) %>% as.data.frame %>% 
+    mutate(name = recode(name, "alpha0" = "c100", "alpha1" = "c101", "gamma0[2]" = "c102",
+                         "gamma0[3]" = "c104", "gamma0[4]" = "c105", "gamma1[2]" = "c106",
+                         "gamma1[3]" = "c107", "gamma1[4]" = "c108", "sigma0" = "c109", "chi" = "c110", "eta" = "c111",
+                         "Eff[2,1]" = "c112", "Eff[3,1]" = "c113", "Eff[4,1]" = "c114", 
+                         "Eff[2,2]" = "c115", "Eff[3,2]" = "c116", "Eff[4,2]" = "c117"))
+
+  titre1 = TeX("$\\alpha_0$");   titre2 = TeX("$\\alpha_1$");   
+
+  titre3 = TeX("$\\gamma_0 - Mavrik Jet$");   titre4 = TeX("$\\gamma_0 - Movento$");   titre5 = TeX("$\\gamma_0 - Teppeki$");   
+  titre6 = TeX("$\\gamma_1 - Mavrik Jet$");   titre7 = TeX("$\\gamma_1 - Movento$");   titre8 = TeX("$\\gamma_1 - Teppeki$");   
+
+  titre9 = TeX("$\\sigma_0$");   titre10 = TeX("$\\chi$");   titre11 = TeX("$\\eta$");   
+
+  titre12 = TeX("$Ef_6 - Mavrik Jet$");   titre13 = TeX("$Ef_6 - Movento$");    titre14 = TeX("$Ef_6 - Teppeki$")
+  titre15 = TeX("$Ef_{12} - Mavrik Jet$");   titre16 = TeX("$Ef_{12} - Movento$");    titre17 = TeX("$Ef_{12} - Teppeki$")
+
+  df_plot = df_plot %>% mutate(name = as.factor(name))
+
+  levels(df_plot$name) = c(titre1, titre2, titre3, titre4, titre5, titre6, titre7, titre8, titre9, titre10, titre11,
+                           titre12, titre13, titre14, titre15, titre16, titre17)
+
+  ggplot(df_plot) + geom_line(aes(x = i, y = value, color = chaine)) + facet_wrap(~ name, scales = "free_y", nrow = nrow, labeller = label_parsed) + theme(legend.position = "none") + xlab("Iteration") + ylab("Sampled value")
+}