diff --git a/R/MFx_ode.survFit.R b/R/MFx_ode.survFit.R
index 4b44349f7ccd93a189b0aafcea947053e9fdb155..ba8c882f9c710bb3d3c941848a1eb4aad0c3f8ed 100644
--- a/R/MFx_ode.survFit.R
+++ b/R/MFx_ode.survFit.R
@@ -80,7 +80,6 @@ MFx_ode <- function(object, ...){
#' from computing survival probability for every profiles build from the vector of
#' multiplication factors \code{MFx_tested}.}
#'
-#'
#' @examples
#'
#' # (1) Load the data
@@ -89,21 +88,6 @@ MFx_ode <- function(object, ...){
#' # (2) Create an object of class 'survData'
#' dataset <- survData(propiconazole)
#'
-#' \donttest{
-#' # (3) Run the survFit function with model_type SD (or IT)
-#' out_SD <- survFit(dataset, model_type = "SD")
-#'
-#' # (4) data to predict
-#' data_4prediction <- data.frame(time = 1:10, conc = c(0,0.5,3,3,0,0,0.5,3,1.5,0))
-#'
-#' # (5) estimate MF(x=30, t=4), that is for 30% reduction of survival at time 4
-#' MFx_SD_30.4 <- MFx_ode(out_SD, data_predict = data_4prediction , X = 30, time_MFx = 4)
-#'
-#' # (5bis) estimate MF(x,t) along the MF_range from 5 to 10 (50) (X = NULL)
-#' MFx_SD_range <- MFx_ode(out_SD, data_predict = data_4prediction ,
-#' X = NULL, time_MFx = 4, MFx_range = seq(5, 10, length.out = 50))
-#' }
-#'
#'
#' @export
#'
@@ -128,14 +112,14 @@ This can take a very long time to compute (minutes to hours).\n
Prefer the function 'MFx' when possible.")
## Analyse data_predict data.frame
- if(!all(colnames(data_predict) %in% c("conc", "time")) || ncol(data_predict) != 2){
+ if (!all(colnames(data_predict) %in% c("conc", "time")) || ncol(data_predict) != 2) {
stop("The argument 'data_predict' is a dataframe with two columns 'time' and 'conc'.")
}
## Check time_MFx
- if(is.null(time_MFx)) time_MFx = max(data_predict$time)
+ if (is.null(time_MFx)) time_MFx = max(data_predict$time)
- if(!(time_MFx %in% data_predict$time)){
+ if (!(time_MFx %in% data_predict$time)) {
stop("Please provide a 'time_MFx' corresponding to a time-point at which concentration is provided.
Interpolation of concentration is too specific to be automatized.")
}
diff --git a/R/morse.R b/R/morse.R
index 39dcd4491ede8471d7de127864ab067d02d98c4b..411019dcc145eba8a61d84e31d590963b9f7f7f3 100644
--- a/R/morse.R
+++ b/R/morse.R
@@ -95,6 +95,7 @@
#' \emph{Scientific Opinion on the state of the art of Toxicokinetic/Toxicodynamic (TKTD) effect models for regulatory risk assessment of pesticides for aquatic organisms}
#' \url{https://www.efsa.europa.eu/en/efsajournal/pub/5377}.
#'
+#' @useDynLib morse, .registration = TRUE
NULL
@@ -416,8 +417,3 @@ NULL
#' \item{\code{replicate}}{A vector of class \code{factor}.} }
#' @keywords data set
NULL
-
-## usethis namespace: start
-#' @useDynLib morse, .registration = TRUE
-## usethis namespace: end
-NULL
diff --git a/R/plot.LCx.R b/R/plot.LCx.R
index f98faf22da1891f1aec5bcd60d4dc62033026183..746db221484a7c3e2b20629db375d8dbb628a7cb 100644
--- a/R/plot.LCx.R
+++ b/R/plot.LCx.R
@@ -1,7 +1,8 @@
-#' Plotting method for \code{LCx} objects
+#' @title Plotting method for \code{LCx} objects
#'
-#' This is the generic \code{plot} S3 method for the
-#' \code{LCx} class. It plots the survival probability as a function of concentration.
+#' @description
+#' This is the generic \code{plot} S3 method for the LCx class.
+#' It plots the survival probability as a function of concentration.
#'
#'
#' @param x An object of class \code{LCx}.
@@ -52,7 +53,7 @@ plot.LCx <- function(x,
time_LCx <- x$time_LCx
# Check if df_LCx are not all NA:
- if(all(is.na(df_LCx$LCx))){
+ if (all(is.na(df_LCx$LCx))) {
warning(paste0("No LCx can be computed at X=", 100-X_prop_provided*100, " and time_LCx=", time_LCx,
"\nSee the grey dotted line on the graph does not cross zone of credible interval.",
"\nUse LCx function 'LCx' with other values for arguments 'time_LCx' (default is the maximum time of the experimental data),
diff --git a/R/plot.MFx.R b/R/plot.MFx.R
index ade568efed5a995e7188af4d8c95d61e0c1c02ae..120ff54449a88160d41d55318f345b74f44e3778 100644
--- a/R/plot.MFx.R
+++ b/R/plot.MFx.R
@@ -1,214 +1,181 @@
-#' Plotting method for \code{MFx} objects
-#'
-#' This is the generic \code{plot} S3 method for the
-#' \code{MFx} class. It plots the survival probability as a function of
-#' the multiplication factor applied or as a function of time.
-#'
-#'
-#' @param x An object of class \code{MFx}.
-#' @param x_variable A character to define the variable for the \eqn{X}-axis,
-#' either \code{"MFx"} or \code{"Time"}. The default is \code{"MFx"}.
-#' @param xlab A label for the \eqn{X}-axis, by default \code{NULL} and depend on the
-#' argument \code{x_variable}.
-#' @param ylab A label for the \eqn{Y}-axis, by default \code{Survival probability median and 95 CI}.
-#' @param main A main title for the plot.
-#' @param log_scale If \code{TRUE}, the x-axis is log-scaled. Default is \code{FALSE}.
-#' @param ncol An interger for the number of columns when several panels are plotted.
-#' @param \dots Further arguments to be passed to generic methods.
-#'
-#' @keywords plot
-#'
-#' @return a plot of class \code{ggplot}
-#'
-#' @examples
-#'
-#' # (1) Load the data
-#' data("propiconazole")
-#'
-#' # (2) Create an object of class 'survData'
-#' dataset <- survData(propiconazole)
-#'
-#' \donttest{
-#' # (3) Run the survFit function with model_type SD (or IT)
-#' out_SD <- survFit(dataset, model_type = "SD")
-#'
-#'# (4) data to predict
-#' data_4prediction <- data.frame(time = 1:10, conc = c(0,0.5,3,3,0,0,0.5,3,1.5,0))
-#'
-#' # (5) estimate MF for 30% reduction of survival at time 4
-#' MFx_SD_30.4 <- MFx(out_SD, data_predict = data_4prediction , X = 30, time_MFx = 4)
-#'
-#' # (6) plot the object of class 'MFx'
-#' plot(MFx_SD_30.4)
-#'
-#' # (6bis) plot with log-scale of x-axis
-#' plot(MFx_SD_30.4, log_scale = TRUE)
-#'
-#' # (6ter) plot with "Time" as the x-axis
-#' plot(MFx_SD_30.4, x_variable = "Time")
-#'
-#' # (7) plot when X = NULL and along a MFx_range from 5 to 10:
-#' MFx_SD_range <- MFx(out_SD, data_predict = data_4prediction ,
-#' X = NULL, time_MFx = 4, MFx_range = seq(5, 10, length.out = 50))
-#' plot(MFx_SD_range)
-#' plot(MFx_SD_range, x_variable = "Time", ncol = 10)
-#' }
-#'
-#' @export
-#'
-#'
-#'
-plot.MFx <- function(x,
- x_variable = "MFx", # other option is "Time"
- xlab = NULL,
- ylab = "Survival probability \n median and 95 CI",
- main = NULL,
- log_scale = FALSE,
- ncol = 3,
- ...){
-
- # definition of xlab and check x_variable
- if(is.null(xlab)){
- if(x_variable == "MFx"){
- xlab = "Multiplication Factor"
- } else if(x_variable == "Time"){
- xlab = "Time"
- } else stop("the argument 'x_variable' must be 'MFx' or 'Time'. The default is 'MFx'.")
- }
-
-
- MFx_plt <- ggplot() + theme_minimal() +
- theme(legend.position = "top",
- legend.title = element_blank())+
- scale_y_continuous(limits = c(0,1))
-
- if(x_variable == "MFx"){
-
- if(is.null(main)){
- main <- paste("Multiplication Factor for MF", x$X_prop_provided*100, "% at time", x$time_MFx)
- }
- if(is.null(x$X_prop)) main <- paste("Survival over [", min(x$MFx_tested), ",", max(x$MFx_tested), "] MF range at time", x$time_MFx)
-
- MFx_plt <- MFx_plt +
- scale_color_manual(values=c("orange", "black", "black")) +
- labs(title = main,
- x = xlab,
- y = ylab) +
- geom_ribbon(data = x$df_dose,
- aes(x = MFx, ymin = qinf95, ymax = qsup95),
- fill = "lightgrey") +
- geom_point(data = x$df_dose,
- aes(x = MFx, y = q50), color = "orange", shape = 4) +
- geom_line(data = x$df_dose,
- aes(x = MFx, y = q50), color = "orange")
-
- if(!is.null(x$X_prop)){
-
- MFx_plt <- MFx_plt +
- geom_point(data = dplyr::filter(x$df_dose, id == "q50"),
- aes(x = MFx, y = q50), color = "orange", shape = 4) +
- geom_point(data = dplyr::filter(x$df_dose, id == "qinf95"),
- aes(x = MFx, y = qinf95), color = "grey", shape = 4) +
- geom_point(data = dplyr::filter(x$df_dose, id == "qsup95"),
- aes(x = MFx, y = qsup95), color = "grey", shape = 4)
-
- legend.point = data.frame(
- x.pts = x$df_MFx$MFx,
- y.pts = rep(x$X_prop, 3),
- pts.leg = c(paste("median: ", round(x$df_MFx$MFx[1],digits = 2)),
- paste("quantile 2.5%: ", round(x$df_MFx$MFx[2],digits = 2)),
- paste("quantile 97.5%: ", round(x$df_MFx$MFx[3],digits = 2)))
- )
-
-
- MFx_plt <- MFx_plt +
- geom_hline(yintercept = x$X_prop, col="grey70", linetype=2) +
- geom_point(data = legend.point,
- aes(x = x.pts, y = y.pts, color = pts.leg))
-
- warning("This is not an error message:
-Just take into account that MFx has been estimated with a binary
-search using the 'accuracy' argument. Cross points indicate the
-position of evaluated time series. To improve the shape of the curve, you
-can use X = NULL, and compute time series around the median MFx, with the
- vector `MFx_range`.")
- }
- if(log_scale == TRUE){
- MFx_plt <- MFx_plt +
- scale_x_log10()
- }
-
- }
-
- if(x_variable == "Time"){
-
- # Plot
- if(is.null(main)) main <- paste("Survival over time. Multiplication Factor of", x$X_prop_provided*100, "percent")
- if(is.null(x$X_prop)) main <- paste("Survival over time")
-
- MFx = x$MFx_tested
-
- k <- 1:length(x$ls_predict)
- #
- # Make a dataframe with quantile of all generated time series
- #
- ls_predict_quantile <- lapply(k, function(kit){
- df_quantile <- x$ls_predict[[kit]]$df_quantile
- df_quantile$MFx <- rep(MFx[[kit]], nrow(x$ls_predict[[kit]]$df_quantile))
- return(df_quantile)
- })
- predict_MFx_quantile <- do.call("rbind", ls_predict_quantile)
-
-
- if(!is.null(x$X_prop)){
-
- initial_predict <- dplyr::filter(predict_MFx_quantile, MFx == 1)
- final_predict <- dplyr::filter(predict_MFx_quantile, MFx == x$df_MFx$MFx[1])
-
- y_arrow <- as.numeric(dplyr::filter(initial_predict, time == x$time_MFx)$q50)
- yend_arrow <- as.numeric(dplyr::filter(final_predict, time == x$time_MFx)$q50)
-
- MFx_plt <- MFx_plt +
- labs(title = main,
- x = xlab,
- y = ylab) +
- # final predict
- geom_ribbon(data = final_predict,
- aes(x = time, ymin = qinf95, ymax = qsup95),
- fill = "grey30", alpha = 0.4) +
- geom_line(data = final_predict,
- aes(x = time, y = q50),
- col="orange", size = 1) +
- # initial predict
- geom_ribbon(data = initial_predict,
- aes(x = time, ymin = qinf95, ymax = qsup95),
- fill = "grey60", alpha = 0.4) +
- geom_line(data = initial_predict,
- aes(x = time, y = q50),
- col="orange", size = 0.3) +
- # arrow
- geom_segment(aes(x = x$time_MFx, y = y_arrow,
- xend = x$time_MFx, yend = yend_arrow),
- arrow = arrow(length = unit(0.2,"cm")))
-
- }
- if(is.null(x$X_prop)){
-
- MFx_plt <- MFx_plt +
- labs(title = main,
- x = xlab,
- y = ylab) +
- geom_ribbon(data = predict_MFx_quantile,
- aes(x = time, ymin = qinf95, ymax = qsup95),
- fill = "grey30", alpha = 0.4) +
- geom_line(data = predict_MFx_quantile,
- aes(x = time, y = q50),
- col="orange", size = 1) +
- facet_wrap( ~ round(MFx, digits = 2), ncol = ncol)
- }
- }
-
-
- return(MFx_plt)
-
-}
+#' Plotting method for \code{MFx} objects
+#'
+#' This is the generic \code{plot} S3 method for the
+#' \code{MFx} class. It plots the survival probability as a function of
+#' the multiplication factor applied or as a function of time.
+#'
+#'
+#' @param x An object of class \code{MFx}.
+#' @param x_variable A character to define the variable for the \eqn{X}-axis,
+#' either \code{"MFx"} or \code{"Time"}. The default is \code{"MFx"}.
+#' @param xlab A label for the \eqn{X}-axis, by default \code{NULL} and depend on the
+#' argument \code{x_variable}.
+#' @param ylab A label for the \eqn{Y}-axis, by default \code{Survival probability median and 95 CI}.
+#' @param main A main title for the plot.
+#' @param log_scale If \code{TRUE}, the x-axis is log-scaled. Default is \code{FALSE}.
+#' @param ncol An interger for the number of columns when several panels are plotted.
+#' @param \dots Further arguments to be passed to generic methods.
+#'
+#' @keywords plot
+#'
+#' @return a plot of class \code{ggplot}
+#'
+#'
+#' @export
+#'
+#'
+#'
+plot.MFx <- function(x,
+ x_variable = "MFx", # other option is "Time"
+ xlab = NULL,
+ ylab = "Survival probability \n median and 95 CI",
+ main = NULL,
+ log_scale = FALSE,
+ ncol = 3,
+ ...){
+
+ # definition of xlab and check x_variable
+ if(is.null(xlab)){
+ if(x_variable == "MFx"){
+ xlab = "Multiplication Factor"
+ } else if(x_variable == "Time"){
+ xlab = "Time"
+ } else stop("the argument 'x_variable' must be 'MFx' or 'Time'. The default is 'MFx'.")
+ }
+
+
+ MFx_plt <- ggplot() + theme_minimal() +
+ theme(legend.position = "top",
+ legend.title = element_blank())+
+ scale_y_continuous(limits = c(0,1))
+
+ if(x_variable == "MFx"){
+
+ if(is.null(main)){
+ main <- paste("Multiplication Factor for MF", x$X_prop_provided*100, "% at time", x$time_MFx)
+ }
+ if(is.null(x$X_prop)) main <- paste("Survival over [", min(x$MFx_tested), ",", max(x$MFx_tested), "] MF range at time", x$time_MFx)
+
+ MFx_plt <- MFx_plt +
+ scale_color_manual(values=c("orange", "black", "black")) +
+ labs(title = main,
+ x = xlab,
+ y = ylab) +
+ geom_ribbon(data = x$df_dose,
+ aes(x = MFx, ymin = qinf95, ymax = qsup95),
+ fill = "lightgrey") +
+ geom_point(data = x$df_dose,
+ aes(x = MFx, y = q50), color = "orange", shape = 4) +
+ geom_line(data = x$df_dose,
+ aes(x = MFx, y = q50), color = "orange")
+
+ if(!is.null(x$X_prop)){
+
+ MFx_plt <- MFx_plt +
+ geom_point(data = dplyr::filter(x$df_dose, id == "q50"),
+ aes(x = MFx, y = q50), color = "orange", shape = 4) +
+ geom_point(data = dplyr::filter(x$df_dose, id == "qinf95"),
+ aes(x = MFx, y = qinf95), color = "grey", shape = 4) +
+ geom_point(data = dplyr::filter(x$df_dose, id == "qsup95"),
+ aes(x = MFx, y = qsup95), color = "grey", shape = 4)
+
+ legend.point = data.frame(
+ x.pts = x$df_MFx$MFx,
+ y.pts = rep(x$X_prop, 3),
+ pts.leg = c(paste("median: ", round(x$df_MFx$MFx[1],digits = 2)),
+ paste("quantile 2.5%: ", round(x$df_MFx$MFx[2],digits = 2)),
+ paste("quantile 97.5%: ", round(x$df_MFx$MFx[3],digits = 2)))
+ )
+
+
+ MFx_plt <- MFx_plt +
+ geom_hline(yintercept = x$X_prop, col="grey70", linetype=2) +
+ geom_point(data = legend.point,
+ aes(x = x.pts, y = y.pts, color = pts.leg))
+
+ warning("This is not an error message:
+Just take into account that MFx has been estimated with a binary
+search using the 'accuracy' argument. Cross points indicate the
+position of evaluated time series. To improve the shape of the curve, you
+can use X = NULL, and compute time series around the median MFx, with the
+ vector `MFx_range`.")
+ }
+ if(log_scale == TRUE){
+ MFx_plt <- MFx_plt +
+ scale_x_log10()
+ }
+
+ }
+
+ if(x_variable == "Time"){
+
+ # Plot
+ if(is.null(main)) main <- paste("Survival over time. Multiplication Factor of", x$X_prop_provided*100, "percent")
+ if(is.null(x$X_prop)) main <- paste("Survival over time")
+
+ MFx = x$MFx_tested
+
+ k <- 1:length(x$ls_predict)
+ #
+ # Make a dataframe with quantile of all generated time series
+ #
+ ls_predict_quantile <- lapply(k, function(kit){
+ df_quantile <- x$ls_predict[[kit]]$df_quantile
+ df_quantile$MFx <- rep(MFx[[kit]], nrow(x$ls_predict[[kit]]$df_quantile))
+ return(df_quantile)
+ })
+ predict_MFx_quantile <- do.call("rbind", ls_predict_quantile)
+
+
+ if(!is.null(x$X_prop)){
+
+ initial_predict <- dplyr::filter(predict_MFx_quantile, MFx == 1)
+ final_predict <- dplyr::filter(predict_MFx_quantile, MFx == x$df_MFx$MFx[1])
+
+ y_arrow <- as.numeric(dplyr::filter(initial_predict, time == x$time_MFx)$q50)
+ yend_arrow <- as.numeric(dplyr::filter(final_predict, time == x$time_MFx)$q50)
+
+ MFx_plt <- MFx_plt +
+ labs(title = main,
+ x = xlab,
+ y = ylab) +
+ # final predict
+ geom_ribbon(data = final_predict,
+ aes(x = time, ymin = qinf95, ymax = qsup95),
+ fill = "grey30", alpha = 0.4) +
+ geom_line(data = final_predict,
+ aes(x = time, y = q50),
+ col="orange", size = 1) +
+ # initial predict
+ geom_ribbon(data = initial_predict,
+ aes(x = time, ymin = qinf95, ymax = qsup95),
+ fill = "grey60", alpha = 0.4) +
+ geom_line(data = initial_predict,
+ aes(x = time, y = q50),
+ col="orange", size = 0.3) +
+ # arrow
+ geom_segment(aes(x = x$time_MFx, y = y_arrow,
+ xend = x$time_MFx, yend = yend_arrow),
+ arrow = arrow(length = unit(0.2,"cm")))
+
+ }
+ if(is.null(x$X_prop)){
+
+ MFx_plt <- MFx_plt +
+ labs(title = main,
+ x = xlab,
+ y = ylab) +
+ geom_ribbon(data = predict_MFx_quantile,
+ aes(x = time, ymin = qinf95, ymax = qsup95),
+ fill = "grey30", alpha = 0.4) +
+ geom_line(data = predict_MFx_quantile,
+ aes(x = time, y = q50),
+ col="orange", size = 1) +
+ facet_wrap( ~ round(MFx, digits = 2), ncol = ncol)
+ }
+ }
+
+
+ return(MFx_plt)
+
+}
diff --git a/tests/testthat/test-predict.R b/tests/testthat/test-predict.R
index 0aded159a64bd84b02ed286aedc79ba58be830e7..b35d55191e4eacd2c725f334ea7de36b5b4b88f1 100644
--- a/tests/testthat/test-predict.R
+++ b/tests/testthat/test-predict.R
@@ -80,51 +80,6 @@ test_that("MCMC longer than one", {
})
-test_that("predict_ode", {
-
- skip_on_cran()
-
- data("propiconazole")
- fit_cstSD <- survFit(survData(propiconazole), quiet = TRUE, model_type = "SD")
-
- data_4prediction <- data.frame(time = c(1:10, 1:10),
- conc = c(c(0,0,40,0,0,0,40,0,0,0),
- c(21,19,18,23,20,14,25,8,13,5)),
- replicate = c(rep("pulse", 10), rep("random", 10)))
-
- # check No ERROR
- expect_error(predict_ode(object = fit_cstSD, data_predict = data_4prediction), NA)
-
-
- data_4MFx <- data.frame(time = 1:10,
- conc = c(0,0.5,8,3,0,0,0.5,8,3.5,0))
- # check No ERROR
- expect_error(MFx(object = fit_cstSD, data_predict = data_4MFx, ode = TRUE), NA)
-
-})
-
-
-test_that("predict_Nsurv_ode internal", {
-
- skip_on_cran()
-
- data("propiconazole")
- fit_cstSD <- survFit(survData(propiconazole), quiet = TRUE, model_type = "SD")
- fit_cstIT <- survFit(survData(propiconazole), quiet = TRUE, model_type = "IT")
-
- data("FOCUSprofile")
- FOCUSprofile$Nsurv = sort(round(runif(nrow(FOCUSprofile), 0, 100)), decreasing = TRUE)
-
- # check No ERROR
- expect_error(predict_Nsurv_ode(object = fit_cstSD, data_predict = FOCUSprofile, mcmc_size = 10), NA)
- expect_error(predict_Nsurv_ode(object = fit_cstIT, data_predict = FOCUSprofile, mcmc_size = 10), NA)
-
- data("propiconazole_pulse_exposure")
- expect_error(predict_Nsurv_ode(fit_cstSD, propiconazole_pulse_exposure, mcmc_size = NULL, interpolate_length = NULL), NA)
- expect_error(predict_Nsurv_ode(fit_cstSD, propiconazole_pulse_exposure, mcmc_size = NULL, interpolate_length = NULL), NA)
-
-})
-
test_that("predict_interpolate", {
data(FOCUSprofile)
diff --git a/tests/testthat/test-repro.R b/tests/testthat/test-repro.R
index f02e1ff6d09212eac53d068369ebf22145b881f9..d11840e619c1bf5f685c329d3c1c6630ad3a2140 100644
--- a/tests/testthat/test-repro.R
+++ b/tests/testthat/test-repro.R
@@ -3,7 +3,7 @@ datasets <- c("cadmium1",
"copper",
"chlordan",
"zinc")
-data(list=datasets)
+data(list = datasets)
failswith_id <- function(dataset, id) {
gen_failswith_id(reproDataCheck, dataset, id)
diff --git a/vignettes/modelling.Rmd b/vignettes/modelling.Rmd
index f7df330af1b9680535a649c886ca2340a9eabb73..f746954b1062d94b74755ff3d8876e5ba2e92c7b 100644
--- a/vignettes/modelling.Rmd
+++ b/vignettes/modelling.Rmd
@@ -85,7 +85,9 @@ using the JAGS software [@rjags2016] with the following priors:
- we assume the range of tested concentrations in an experiment is
chosen to contain the $LC_{50}$ with high probability. More
formally, we choose:
- $$\log_{10} e \sim \mathcal{N}\left(\frac{\log_{10} (\min_i c_i) + \log_{10} (\max_i c_i)}{2}, \frac{\log_{10} (\max_i c_i) - \log_{10} (\min_i c_i)}{4} \right)$$
+ $$\log_{10} e \sim \mathcal{N}\left(\frac{\log_{10} (\min_i c_i) +
+ \log_{10} (\max_i c_i)}{2}, \frac{\log_{10} (\max_i c_i) -
+ \log_{10} (\min_i c_i)}{4} \right)$$
which implies $e$ has a probability slightly higher than 0.95 to lie
between the minimum and the maximum tested concentrations.
- we choose a quasi non-informative prior distribution for the shape