R Under development (unstable) (2026-05-11 r90046 ucrt) -- "Unsuffered Consequences"
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> library(BayesPPR)
> f <- function(xx)
+ {
+   ##########################################################################
+   #
+   # WELCH ET AL. (1992) FUNCTION
+   #
+   # Authors: Sonja Surjanovic, Simon Fraser University
+   #          Derek Bingham, Simon Fraser University
+   # Questions/Comments: Please email Derek Bingham at dbingham@stat.sfu.ca.
+   #
+   # Copyright 2013. Derek Bingham, Simon Fraser University.
+   #
+   # THERE IS NO WARRANTY, EXPRESS OR IMPLIED. WE DO NOT ASSUME ANY LIABILITY
+   # FOR THE USE OF THIS SOFTWARE.  If software is modified to produce
+   # derivative works, such modified software should be clearly marked.
+   # Additionally, this program is free software; you can redistribute it
+   # and/or modify it under the terms of the GNU General Public License as
+   # published by the Free Software Foundation; version 2.0 of the License.
+   # Accordingly, this program is distributed in the hope that it will be
+   # useful, but WITHOUT ANY WARRANTY; without even the implied warranty
+   # of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
+   # General Public License for more details.
+   #
+   # For function details and reference information, see:
+   # http://www.sfu.ca/~ssurjano/
+   #
+   ##########################################################################
+   #
+   # INPUT:
+   #
+   # xx = c(x1, x2, ..., 20)
+   #
+   ##########################################################################
+ 
+   x1  <- xx[1] - 0.5
+   x2  <- xx[2] - 0.5
+   x3  <- xx[3] - 0.5
+   x4  <- xx[4] - 0.5
+   x5  <- xx[5] - 0.5
+   x6  <- xx[6] - 0.5
+   x7  <- xx[7] - 0.5
+   x8  <- xx[8] - 0.5
+   x9  <- xx[9] - 0.5
+   x10 <- xx[10] - 0.5
+   x11 <- xx[11] - 0.5
+   x12 <- xx[12] - 0.5
+   x13 <- xx[13] - 0.5
+   x14 <- xx[14] - 0.5
+   x15 <- xx[15] - 0.5
+   x16 <- xx[16] - 0.5
+   x17 <- xx[17] - 0.5
+   x18 <- xx[18] - 0.5
+   x19 <- xx[19] - 0.5
+   x20 <- xx[20] - 0.5
+ 
+   term1 <- 5*x12 / (1+x1)
+   term2 <- 5 * (x4-x20)^2
+   term3 <- x5 + 40*x19^3 - 5*x19
+   term4 <- 0.05*x2 + 0.08*x3 - 0.03*x6
+   term5 <- 0.03*x7 - 0.09*x9 - 0.01*x10
+   term6 <- -0.07*x11 + 0.25*x13^2 - 0.04*x14
+   term7 <- 0.06*x15 - 0.01*x17 - 0.03*x18
+ 
+   y <- term1 + term2 + term3 + term4 + term5 + term6 + term7
+   return(y)
+ }
> 
> 
> set.seed(71023)
> n <- 5000
> p <- 20
> X <- matrix(runif(n*p), n)
> y <- apply(X, 1, f) + rnorm(n, sd = 0.2)
> 
> fit <- bppr(X, y)
MCMC iteration 1/10000 (burn) -- May 12 23:50:49 -- n ridge: 0
MCMC iteration 1001/10000 (burn) -- 2.47 secs -- n ridge: 16 
MCMC iteration 2001/10000 (burn) -- 5.27 secs -- n ridge: 14 
MCMC iteration 3001/10000 (burn) -- 8.09 secs -- n ridge: 14 
MCMC iteration 4001/10000 (burn) -- 10.92 secs -- n ridge: 14 
MCMC iteration 5001/10000 (burn) -- 13.7 secs -- n ridge: 15 
MCMC iteration 6001/10000 (burn) -- 16.45 secs -- n ridge: 14 
MCMC iteration 7001/10000 (burn) -- 19.16 secs -- n ridge: 14 
MCMC iteration 8001/10000 (burn) -- 22.02 secs -- n ridge: 15 
MCMC iteration 9001/10000 (post-burn) -- 24.79 secs -- n ridge: 14 
MCMC iteration 10000/10000 (post-burn) -- 27.5 secs -- n ridge: 14
> plot(fit$sd_resid, type = 'l')
> 
> X_test <- matrix(runif(n*p), n)
> preds <- predict(fit, X_test)
> pred_mn <- apply(preds, 2, mean)
> plot(apply(X_test, 1, f), pred_mn)
> abline(0, 1, col = 2)
> sqrt(mean((apply(X_test, 1, f) - pred_mn)^2))
[1] 0.05404021
> 
> 
> 
> proc.time()
   user  system elapsed 
  22.12    7.78   29.90