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Generate Data
f<-function(x){
10*sin(pi*x[,1]*x[,2])+20*(x[,3]-.5)^2+10*x[,4]+5*x[,5]
}
sigma<-1
nfunc = 50
tt = seq(0, 1, length.out = nfunc) # functional variable grid
n = 500 # sample size
p = 9 # number of predictors other (only 4 are used)
X<-matrix(runif(n*p),n,p) # 9 non-functional variables, only first 4 matter
x<-cbind(rep(tt,each=n),kronecker(rep(1,nfunc),X)) # to get y
Y<-matrix(f(x),nrow=n)+rnorm(n*nfunc,0,sigma)
ntest = 1000
Xtest = matrix(runif(ntest * p), ntest, p)
x<-cbind(rep(tt,each=ntest),kronecker(rep(1,nfunc),Xtest)) # to get y
Ytest = matrix(f(x),nrow=ntest)+rnorm(ntest*nfunc,0,sigma)Fit a multivariate BASS model
mod = mvBayes(
bass,
X,
Y,
nBasis=3
)
#> Starting mvBayes with 3 components, using 1 cores.
#> MCMC Start #-- Jul 30 11:58:19 --# nbasis: 0
#> MCMC iteration 1000 #-- Jul 30 11:58:19 --# nbasis: 14
#> MCMC iteration 2000 #-- Jul 30 11:58:19 --# nbasis: 12
#> MCMC iteration 3000 #-- Jul 30 11:58:20 --# nbasis: 12
#> MCMC iteration 4000 #-- Jul 30 11:58:20 --# nbasis: 12
#> MCMC iteration 5000 #-- Jul 30 11:58:20 --# nbasis: 12
#> MCMC iteration 6000 #-- Jul 30 11:58:20 --# nbasis: 12
#> MCMC iteration 7000 #-- Jul 30 11:58:20 --# nbasis: 12
#> MCMC iteration 8000 #-- Jul 30 11:58:20 --# nbasis: 12
#> MCMC iteration 9000 #-- Jul 30 11:58:20 --# nbasis: 12
#> MCMC iteration 10000 #-- Jul 30 11:58:20 --# nbasis: 12
#> MCMC Start #-- Jul 30 11:58:20 --# nbasis: 0
#> MCMC iteration 1000 #-- Jul 30 11:58:21 --# nbasis: 7
#> MCMC iteration 2000 #-- Jul 30 11:58:21 --# nbasis: 8
#> MCMC iteration 3000 #-- Jul 30 11:58:21 --# nbasis: 5
#> MCMC iteration 4000 #-- Jul 30 11:58:21 --# nbasis: 5
#> MCMC iteration 5000 #-- Jul 30 11:58:21 --# nbasis: 4
#> MCMC iteration 6000 #-- Jul 30 11:58:21 --# nbasis: 4
#> MCMC iteration 7000 #-- Jul 30 11:58:21 --# nbasis: 5
#> MCMC iteration 8000 #-- Jul 30 11:58:21 --# nbasis: 4
#> MCMC iteration 9000 #-- Jul 30 11:58:21 --# nbasis: 4
#> MCMC iteration 10000 #-- Jul 30 11:58:22 --# nbasis: 4
#> MCMC Start #-- Jul 30 11:58:22 --# nbasis: 0
#> MCMC iteration 1000 #-- Jul 30 11:58:22 --# nbasis: 8
#> MCMC iteration 2000 #-- Jul 30 11:58:22 --# nbasis: 8
#> MCMC iteration 3000 #-- Jul 30 11:58:22 --# nbasis: 6
#> MCMC iteration 4000 #-- Jul 30 11:58:22 --# nbasis: 7
#> MCMC iteration 5000 #-- Jul 30 11:58:22 --# nbasis: 7
#> MCMC iteration 6000 #-- Jul 30 11:58:22 --# nbasis: 7
#> MCMC iteration 7000 #-- Jul 30 11:58:22 --# nbasis: 7
#> MCMC iteration 8000 #-- Jul 30 11:58:22 --# nbasis: 7
#> MCMC iteration 9000 #-- Jul 30 11:58:22 --# nbasis: 7
#> MCMC iteration 10000 #-- Jul 30 11:58:23 --# nbasis: 7
#> Generating 'samples' attribute, since it was absent in 'bmList[[1]]'
#> Approximating 'residSD', since 'residSDExtract' is None
plot(mod)
#> Warning in predict.mvBayes(x, Xtest, returnPostCoefs = TRUE, idxSamples =
#> idxSamples): 'idxSamples' is not an argument of the bayesModel predict
#> function...setting idxSamples='default'
Plot PCA Decomposition
Plot Traceplots
Evaluate Training Fit
plot(mod, idxMV = tt, xlabel = "tt")
#> Warning in predict.mvBayes(x, Xtest, returnPostCoefs = TRUE, idxSamples =
#> idxSamples): 'idxSamples' is not an argument of the bayesModel predict
#> function...setting idxSamples='default'
Evaluate Test Fit
plot(mod, Xtest = Xtest, Ytest = Ytest, idxMV = tt, xlabel = "tt")
#> Warning in predict.mvBayes(x, Xtest, returnPostCoefs = TRUE, idxSamples =
#> idxSamples): 'idxSamples' is not an argument of the bayesModel predict
#> function...setting idxSamples='default'
Compute Sensitivity
modSensitivity = mvSobol(mod)
#> Start ##------ Thu Jul 30 11:58:28 2026 ------##
#> Integrating ##------ Thu Jul 30 11:58:28 2026 ------##
#> Shuffling ##------ Thu Jul 30 11:58:28 2026 ------##
#> Finish ##------ Thu Jul 30 11:58:28 2026 ------##
#> Warning in mvSobol(mod): 'BASS' has not implemented totalOrder
plot(modSensitivity, idxMV = tt, xlabel = "tt")
#> Warning in plot.sobol(modSensitivity, idxMV = tt, xlabel = "tt"): 'x' does not
#> have totalOrderSobol
Compute Posterior Samples and Means
# All posterior predictive samples
Ytest_postSamples = predict(mod, Xtest)
# Posterior predictive mean
Ytest_postMean = apply(Ytest_postSamples, 2, mean)
# single posterior predictive sample (from MCMC iteration #429)
Ytest_postSample429 = predict(mod, Xtest, idxSamples = 429)
#> Warning in predict.mvBayes(mod, Xtest, idxSamples = 429): 'idxSamples' is not
#> an argument of the bayesModel predict function...setting idxSamples='default'These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.
Health stats visible at Monitor.