# NOT RUN {
## This example shows how to run and calibrate the VSEM model
library(BayesianTools)
# Create input data for the model
PAR <- VSEMcreatePAR(1:1000)
plotTimeSeries(observed = PAR)
# load reference parameter definition (upper, lower prior)
refPars <- VSEMgetDefaults()
# this adds one additional parameter for the likelihood standard deviation (see below)
refPars[12,] <- c(2, 0.1, 4)
rownames(refPars)[12] <- "error-sd"
head(refPars)
# create some simulated test data
# generally recommended to start with simulated data before moving to real data
referenceData <- VSEM(refPars$best[1:11], PAR) # model predictions with reference parameters
referenceData[,1] = 1000 * referenceData[,1]
# this adds the error - needs to conform to the error definition in the likelihood
obs <- referenceData + rnorm(length(referenceData), sd = refPars$best[12])
oldpar <- par(mfrow = c(2,2))
for (i in 1:4) plotTimeSeries(observed = obs[,i],
predicted = referenceData[,i], main = colnames(referenceData)[i])
# Best to program in a way that we can choose easily which parameters to calibrate
parSel = c(1:6, 12)
# here is the likelihood
likelihood <- function(par, sum = TRUE){
# set parameters that are not calibrated on default values
x = refPars$best
x[parSel] = par
predicted <- VSEM(x[1:11], PAR) # replace here VSEM with your model
predicted[,1] = 1000 * predicted[,1] # this is just rescaling
diff <- c(predicted[,1:4] - obs[,1:4]) # difference betweeno observed and predicted
# univariate normal likelihood. Note that there is a parameter involved here that is fit
llValues <- dnorm(diff, sd = x[12], log = TRUE)
if (sum == FALSE) return(llValues)
else return(sum(llValues))
}
# optional, you can also directly provide lower, upper in the createBayesianSetup, see help
prior <- createUniformPrior(lower = refPars$lower[parSel],
upper = refPars$upper[parSel], best = refPars$best[parSel])
bayesianSetup <- createBayesianSetup(likelihood, prior, names = rownames(refPars)[parSel])
# settings for the sampler, iterations should be increased for real applicatoin
settings <- list(iterations = 2000, nrChains = 2)
out <- runMCMC(bayesianSetup = bayesianSetup, sampler = "DEzs", settings = settings)
# }
# NOT RUN {
plot(out)
summary(out)
marginalPlot(out, scale = T)
gelmanDiagnostics(out) # should be below 1.05 for all parameters to demonstrate convergence
# Posterior predictive simulations
# Create a prediction function
createPredictions <- function(par){
# set the parameters that are not calibrated on default values
x = refPars$best
x[parSel] = par
predicted <- VSEM(x[1:11], PAR) # replace here VSEM with your model
return(predicted[,1] * 1000)
}
# Create an error function
createError <- function(mean, par){
return(rnorm(length(mean), mean = mean, sd = par[7]))
}
# plot prior predictive distribution and prior predictive simulations
plotTimeSeriesResults(sampler = out, model = createPredictions, observed = referenceData[,1],
error = createError, prior = TRUE, main = "Prior predictive")
# plot posterior predictive distribution and posterior predictive simulations
plotTimeSeriesResults(sampler = out, model = createPredictions, observed = referenceData[,1],
error = createError, main = "Posterior predictive")
########################################################
# Demonstrating the updating of the prior from old posterior
# Note that it is usually more exact to rerun the MCMC
# with all (old and new) data, instead of updating the prior
# because likely some information is lost when approximating the
# Posterior by a multivariate normal
settings <- list(iterations = 5000, nrChains = 2)
out <- runMCMC(bayesianSetup = bayesianSetup, sampler = "DEzs", settings = settings)
plot(out)
correlationPlot(out, start = 1000)
newPrior = createPriorDensity(out, method = "multivariate",
eps = 1e-10,
lower = refPars$lower[parSel],
upper = refPars$upper[parSel], start= 1000)
bayesianSetup <- createBayesianSetup(likelihood = likelihood,
prior = newPrior,
names = rownames(refPars)[parSel] )
# check boundaries are correct set
bayesianSetup$prior$sampler() < refPars$lower[parSel]
bayesianSetup$prior$sampler() > refPars$upper[parSel]
# check prior looks similar to posterior
x = bayesianSetup$prior$sampler(2000)
correlationPlot(x, thin = F)
out <- runMCMC(bayesianSetup = bayesianSetup, sampler = "DEzs", settings = settings)
plot(out)
correlationPlot(out)
plotTimeSeriesResults(sampler = out,
model = createPredictions,
observed = referenceData[,1],
error = createError,
prior = F, main = "Posterior predictive")
plotTimeSeriesResults(sampler = out,
model = createPredictions,
observed = referenceData[,1],
error = createError,
prior = T, main = "Prior predictive")
# }
# NOT RUN {
par(oldpar)
# }
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