Sensitivity Ranges of a Timeseries or 1-D Variables
Given a model consisting of differential equations, estimates the global effect of certain (sensitivity) parameters on a time series or on 1-D spatial series of selected sensitivity variables.
This is done by drawing parameter values according to some predefined distribution, running the model with each of these parameter combinations, and calculating the values of the selected output variables at each output interval.
This function thus produces 'envelopes' around the sensitivity variables.
sensRange(func, parms = NULL, sensvar = NULL, dist = "unif",
parInput = NULL, parRange = NULL, parMean = NULL,
parCovar = NULL, map = 1, num = 100, ...)
## S3 method for class 'sensRange'
summary(object, ...)
## S3 method for class 'summary.sensRange'
plot(x, xyswap = FALSE,
which = NULL, legpos = "topleft",
col = c(grey(0.8), grey(0.7)),
quant = FALSE, ask = NULL, obs = NULL,
obspar = list(), ...)
## S3 method for class 'sensRange'
plot(x, xyswap = FALSE,
which = NULL, ask = NULL, ...)func |
an R-function that has as first argument |
parms |
parameters passed to |
sensvar |
the output variables for which the sensitivity needs
to be estimated. Either |
dist |
the distribution according to which the parameters should be
generated, one of |
parRange |
the range (min, max) of the sensitivity parameters, a
matrix or (preferred) a data.frame with one row for each parameter,
and two columns with the minimum (1st) and maximum (2nd) value. The
rownames of |
parInput |
a matrix with dimension (*, npar) with the values of the sensitivity parameters. |
parMean |
only when |
parCovar |
only when |
num |
the number of times the model has to be run. Set large
enough. If |
map |
the column number with the (independent) mapping variable
in the output matrix returned by |
object |
an object of class |
x |
an object of class |
legpos |
position of the legend; set to |
xyswap |
if |
which |
the name or the index to the variables that should be plotted. Default = all variables. |
col |
the two colors of the polygons that should be plotted. |
quant |
if |
ask |
logical; if |
obs |
a |
obspar |
additional graphics arguments passed to |
... |
additional arguments passed to |
Models solved by integration (i.e. by using one of 'ode', 'ode.1D',
'ode.band', 'ode.2D'), have the output already in a form usable by
sensRange.
a data.frame of type sensRange containing the parameter
set and the corresponding values of the sensitivity output variables.
The following methods are included:
summary, estimates summary statistics for the
sensitivity variables, a data.frame with as many rows as there are
mapping variables (or rows in the matrix returned by func)
and the following columns: x, the mapping value,
Mean, the mean, sd, the standard deviation,
Min, the minimal value, Max, the maximal value,
q25, q50, q75, the 25th, 50 and 75% quantile
plot, produces a "matplot" of the sensRange
output, one plot for each sensitivity variable and with the
mapping variable on the x-axis.
Each variable will be plotted in a separate figure, and the
figures aligned in a rectangular grid, unless par mfrow is
passed as an argument.
summary.plot, produces a plot of the summary of the
sensRange output, one plot for each sensitivity variable
and with the ranges and mean +- standard deviation or the
quantiles as coloured polygons.
Each variable will be plotted in a separate figure, and the
figures aligned in a rectangular grid, unless par mfrow is
passed as an argument.
The output for models solved by a steady-state solver (i.e. one of
'steady', 'steady.1D', 'steady.band', 'steady.2D', needs to be
rearranged – see examples.
For plot.summary.sensRange and plot.sensRange,
the number of panels per page is automatically determined up to 3 x 3
(par(mfrow = c(3, 3))). This default can be overwritten by
specifying user-defined settings for mfrow or mfcol.
Set mfrow equal to NULL to avoid the plotting function to
change user-defined mfrow or mfcol settings.
Other graphical parameters can be passed as well. Parameters
are vectorized, either according to the number of plots
(xlab, ylab, main, sub, xlim, ylim, log,
asp, ann, axes, frame.plot,panel.first,panel.last,
cex.lab,cex.axis,cex.main) or
according to the number of lines within one plot (other parameters
e.g. col, lty, lwd etc.) so it is possible to
assign specific axis labels to individual plots, resp. different plotting
style. Plotting parameter ylim, or xlim can also be a list
to assign different axis limits to individual plots.
Similarly, the graphical parameters for observed data, as passed by
obspar can be vectorized, according to the number of observed
data sets (when obs is a list).
The data.frame of type sensRange has several attributes,
which remain hidden, and which are generally not of practical use
(they are needed for the S3 methods).
There is one exception, i.e. if parameter values are imposed via
argument parInput, and these parameters are generated by a
Markov chain (modMCMC). If the number of draws,
num, is less than the number of rows in parInput, then
num random draws will be taken. Attribute, "pset" then contains
the index to the parameters that have been selected.
The sensRange method only represents the distribution of the
model response variables as a function of the parameter values. But an
additional source of noise is due to the model error, as
represented by the sampled values of sigma in the Markov chain. In
order to represent also this source of error, gaussian noise should be
added to each sensitivity output variables, with a standard deviation
that corresponds to the original parameter draw – see vignette
"FMEother".
Karline Soetaert <karline.soetaert@nioz.nl>
Soetaert, K. and Petzoldt, T., 2010. Inverse Modelling, Sensitivity and Monte Carlo Analysis in R Using Package FME. Journal of Statistical Software 33(3) 1–28. http://www.jstatsoft.org/v33/i03
## =======================================================================
## Bacterial growth model from Soetaert and Herman, 2009
## =======================================================================
pars <- list(gmax = 0.5,eff = 0.5,
ks = 0.5, rB = 0.01, dB = 0.01)
solveBact <- function(pars) {
derivs <- function(t,state,pars) { # returns rate of change
with (as.list(c(state,pars)), {
dBact <- gmax*eff * Sub/(Sub + ks)*Bact - dB*Bact - rB*Bact
dSub <- -gmax * Sub/(Sub + ks)*Bact + dB*Bact
return(list(c(dBact,dSub)))
})
}
state <- c(Bact = 0.1,Sub = 100)
tout <- seq(0, 50, by = 0.5)
## ode solves the model by integration ...
return(as.data.frame(ode(y = state, times = tout, func = derivs,
parms = pars)))
}
out <- solveBact(pars)
mf <-par(mfrow = c(2,2))
plot(out$time, out$Bact, main = "Bacteria",
xlab = "time, hour", ylab = "molC/m3", type = "l", lwd = 2)
## the sensitivity parameters
parRanges <- data.frame(min = c(0.4, 0.4, 0.0), max = c(0.6, 0.6, 0.02))
rownames(parRanges)<- c("gmax", "eff", "rB")
parRanges
tout <- 0:50
## sensitivity to rB; equally-spaced parameters ("grid")
SensR <- sensRange(func = solveBact, parms = pars, dist = "grid",
sensvar = "Bact", parRange = parRanges[3,], num = 50)
Sens <-summary(SensR)
plot(Sens, legpos = "topleft", xlab = "time, hour", ylab = "molC/m3",
main = "Sensitivity to rB", mfrow = NULL)
## sensitivity to all; latin hypercube
Sens2 <- summary(sensRange(func = solveBact, parms = pars, dist = "latin",
sensvar = c("Bact", "Sub"), parRange = parRanges, num = 50))
## Plot all variables; plot mean +- sd, min max
plot(Sens2, xlab = "time, hour", ylab = "molC/m3",
main = "Sensitivity to gmax,eff,rB", mfrow = NULL)
par(mfrow = mf)
## Select one variable for plotting; plot the quantiles
plot(Sens2, xlab = "time, hour", ylab = "molC/m3", which = "Bact", quant = TRUE)
## Add data
data <- cbind(time = c(0,10,20,30), Bact = c(0,1,10,45))
plot(Sens2, xlab = "time, hour", ylab = "molC/m3", quant = TRUE,
obs = data, obspar = list(col = "darkblue", pch = 16, cex = 2))Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.