# Bayesian Adaptive Spline Surfaces (BASS) with PCA decomposition of response Decomposes a multivariate or functional response onto a principal component basis and fits a BASS model to each basis coefficient. ```r bassPCA( xx = NULL, y = NULL, dat = NULL, n.pc = NULL, perc.var = 99, n.cores = 1, parType = "fork", center = T, scale = F, ... ) ``` ## Arguments - `xx`: a data frame or matrix of predictors with dimension n x p. Categorical predictors should be included as factors. - `y`: a response matrix (functional response) with dimension n x m. - `dat`: optional (for more control) list with elements `xx` (same as above), `y` (same as above), `n.pc` (number of principal components used), `basis` (principal components with dimension m x `n.pc`), `newy` (reduced dimension `y` with dimension `n.pc` x n), `trunc.error` (optional truncation error with dimension n x m), `y.m` (vector mean removed before PCA with dimension m), `y.s` (vector sd scaled before PCA with dimension m). If `dat` is specified, `xx`, `y` and `n.pc` do not need to be specified. - `n.pc`: number of principal components to use - `perc.var`: optionally specify percent of variance to explain instead of n.pc - `n.cores`: integer number of cores (threads) to use - `parType`: either "fork" or "socket". Forking is typically faster, but not compatible with Windows. If `n.cores==1`, `parType` is ignored. - `center`: logical whether to subtract the mean before getting the principal components, or else a numeric vector of dimension m for the center to be used - `scale`: logical whether to divide by the standard deviation before getting the principal components, or else a numeric vector of dimension m for the scale to be used - `...`: arguements to be passed to `bass` function calls. ## Returns An object of class 'bassBasis' with two elements: - **mod.list**: list (of length `n.pc`) of individual bass models - **dat**: same as dat above ## Details Gets the PCA decomposition of the response `y`, and fits a bass model to each PCA basis coefficient, `bass(dat$xx,dat$newy[i,],...)` for `i in 1 to n.pc`, possibly in parallel. ## Examples ```r ## Not run: ## simulate data (Friedman function) f<-function(x){ 10*sin(pi*x[,1]*x[,2])+20*(x[,3]-.5)^2+10*x[,4]+5*x[,5] } ## simulate data (Friedman function with first variable as functional) sigma<-.1 # noise sd n<-500 # number of observations nfunc<-50 # size of functional variable grid xfunc<-seq(0,1,length.out=nfunc) # functional grid x<-matrix(runif(n*9),n,9) # 9 non-functional variables, only first 4 matter X<-cbind(rep(xfunc,each=n),kronecker(rep(1,nfunc),x)) # to get y y<-matrix(f(X),nrow=n)+rnorm(n*nfunc,0,sigma) ## fit BASS library(parallel) mod<-bassPCA(x,y,n.pc=5,n.cores=min(5,parallel::detectCores())) plot(mod$mod.list[[1]]) plot(mod$mod.list[[2]]) plot(mod$mod.list[[3]]) plot(mod$mod.list[[4]]) plot(mod$mod.list[[5]]) hist(mod$dat$trunc.error) ## prediction npred<-100 xpred<-matrix(runif(npred*9),npred,9) Xpred<-cbind(rep(xfunc,each=npred),kronecker(rep(1,nfunc),xpred)) ypred<-matrix(f(Xpred),nrow=npred) pred<-predict(mod,xpred,mcmc.use=1:1000) # posterior predictive samples (each is a curve) matplot(ypred,apply(pred,2:3,mean),type='l',xlab='observed',ylab='mean prediction') abline(a=0,b=1,col=2) matplot(t(ypred),type='l') # actual matplot(t(apply(pred,2:3,mean)),type='l') # mean prediction ## sensitivity sens<-sobolBasis(mod,int.order = 2,ncores = max(parallel::detectCores()-2,1), mcmc.use=1000) # for speed, only use a few samples plot(sens) ## calibration x.true<-runif(9,0,1) # what we are trying to learn yobs<-f(cbind(xfunc,kronecker(rep(1,nfunc),t(x.true)))) + rnorm(nfunc,0,.1) # calibration data (with measurement error) plot(yobs) cal<-calibrate.bassBasis(y=yobs,mod=mod, discrep.mean=rep(0,nfunc), discrep.mat=diag(nfunc)[,1:2]*.0000001, sd.est=.1, s2.df=50, s2.ind=rep(1,nfunc), meas.error.cor=diag(nfunc), bounds=rbind(rep(0,9),rep(1,9)), nmcmc=10000, temperature.ladder=1.05^(0:30),type=1) nburn<-5000 uu<-seq(nburn,10000,5) pairs(rbind(cal$theta[uu,1,],x.true),col=c(rep(1,length(uu)),2),ylim=c(0,1),xlim=c(0,1)) pred<-apply(predict(mod,cal$theta[uu,1,],nugget = T,trunc.error = T, mcmc.use = cal$ii[uu]),3,function(x) diag(x)+rnorm(length(uu),0,sqrt(cal$s2[uu,1,1]))) qq<-apply(pred,2,quantile,probs=c(.025,.975)) matplot(t(qq),col='lightgrey',type='l') lines(yobs,lwd=3) ## End(Not run) ## minimal example for CRAN testing mod<-bassPCA(1:10,matrix(1:20,10),n.pc=2,nmcmc=2,nburn=1) ``` ## See Also predict.bassBasis for prediction and sobolBasis for sensitivity analysis.

bassPCA function