---
title: "friedman_demo"
output: rmarkdown::html_vignette
vignette: >
  %\VignetteIndexEntry{friedman_demo}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---

```{r, include = FALSE}
knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>"
)
knitr::opts_chunk$set(fig.width = 6, fig.height = 6)
```

```{r setup}
library(mvBayes)
library(BASS)
```

Generate Data
```{r 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

```{r bass}
mod = mvBayes(
  bass,
  X,
  Y,
  nBasis=3
)
plot(mod)
```

Plot PCA Decomposition
```{r pca}
plot(mod$basisInfo, idxMV = tt, xlabel = "tt") 
```

Plot Traceplots
```{r traceplot}
traceplot(mod)
```

Evaluate Training Fit
```{r train}
plot(mod, idxMV = tt, xlabel = "tt")
```

Evaluate Test Fit
```{r test}
plot(mod, Xtest = Xtest, Ytest = Ytest, idxMV = tt, xlabel = "tt")
```

Compute Sensitivity
```{r sobol}
modSensitivity = mvSobol(mod)
plot(modSensitivity, idxMV = tt, xlabel = "tt")
```

Compute Posterior Samples and Means
```{r posterior}
# 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)
```