predict.rbart: Drawing Posterior Predictive Realizations for rbart models.

In rbart: Bayesian Trees for Conditional Mean and Variance

Description

The function predict.rbart() is the main function for drawing posterior predictive realizations at new inputs using a fitted model stored in a rbart object returned from rbart().

Usage

## S3 method for class 'rbart'
predict(
object,
x.test=object$x.train,
tc=1,
fmean=mean(object$y.train),
q.lower=0.025,
q.upper=0.975,...)

Arguments

object	Object of type rbart from a previous call to rbart()
x.test	New input settings in the form of an npred x p matrix at which to construct predictions. Defaults to the training inputs.
tc	Number of OpenMP threads to use for parallel computing.
fmean	Mean-centering vector for the training data. Defaults to the value used by rbart() when fitting the model. Usually should be left to the default.
q.lower	Lower quantile to return.
q.upper	Upper quantile to return.
...	not used.

Details

predict.rbart() is the main function for calculating posterior predictions and uncertainties once a model has been fit by rbart().

Returns an object of type rbart with the following entries.

Value

mdraws	Posterior realizations of the mean function, f(x) stored in an ndpost x npred matrix, where ndpost is the number of kept MCMC draws in the rbart run.
sdraws	Posterior realizations of the standard deviation function, s(x) stored in an ndpost x npred matrix, where ndpost is the number of kept MCMC draws in the rbart run.
mmean	Posterior predictive mean of f(x).
smean	Posterior predictive mean of the standard deviation, s(x).
msd	Posterior standard deviation of the mean, f(x).
ssd	Posterior standard deviation of the standard devation, s(x).
m.5	Posterior median of the mean function realizations, f(x).
m.lower	Posterior q.lower quantile of the mean function realizations.
m.upper	Posterior q.upper quantile of the mean function realizations.
s.5	Posterior median of the standard deviation function realizations, s(x).
s.lower	Posterior q.lower quantile of the standard deviation function realizations.
s.upper	Posterior q.upper quantile of the standard deviation function realizations.
q.lower	Lower quantile used in constructing the above.
q.upper	Upper quantile used in constructing the above.

Author(s)

Matthew T. Pratola <[e-mail]> [aut, cre, cph], Robert E. McCulloch <[e-mail]> [aut, cre, cph], Hugh Chipman <[e-mail]> [aut, cph] Maintainer: Matthew T. Pratola <[e-mail]>, Robert E. McCulloch <[e-mail]>

References

Chipman, Hugh A., George, Edward I., and McCulloch, Robert E. (1998) Bayesian CART model search. Journal of the American Statistical Association, 93, 935–948.

Chipman, Hugh A., George, Edward I., and McCulloch, Robert E. (2010) BART: Bayesian additive regression trees. The Annals of Applied Statistics, 4, 266–298.

Pratola, Matthew T. (2016) Efficient Metropolis Hastings proposal mechanisms for Bayesian regression tree models. Bayesian analysis, 11, 885–911.

Pratola, Matthew T., Chipman, Hugh A., George, Edward I. and McCulloch, Robert E. (2017) Heteroscedastic BART Using Multiplicative Regression Trees. arXiv preprint, arXiv:1709.07542, 1–20.

See Also

rbart

Examples

##################################################
## This is just a stub (runs fast) example for testing.
##  For more realistic examples, please see:
##   (i) the vignette at www.rob-mcculloch.org
##   (ii) the example simulated data (see ?simdat)
##        and the longer run in ?rbartonsimd, 
##        where a saved run of rbart is run on simdat is plotted. 
##################################################

##simulate data
set.seed(99)

# train data
n=500 #train data sample size
p=1 #just one x
x = matrix(sort(runif(n*p)),ncol=p) #iid uniform x values
fx = 4*(x[,1]^2) #quadratric function f
sx = .2*exp(2*x[,1]) # exponential function s
y = fx + sx*rnorm(n) # y = f(x) + s(x) Z

#test data (the p added to the variable names is for predict)
np=500 #test data sample size
xp = matrix(sort(runif(np*p)),ncol=p)
fxp = 4*(xp[,1]^2)
sxp = .2*exp(2*xp[,1])
yp = fxp + sxp*rnorm(np)

##run rbart MCMC
# The number of interations is kept small to make example run,
##!!!!  REAL APPLICATIONS MAY NEED LONGER RUNS !!!!
#   nskip: burn in draws,
#   ndpost:kept draws,
#   nadapt: initial draws to tune MCMC,
#   numcut: number of cutpoints used for each x
#   k: bigger k gives smoother f (default is 2)
set.seed(19)
res = rbart(x,y,nskip=10,ndpost=20,nadapt=0,numcut=1000,k=5) #again, this is way too short a run!!!
## now predict to get inference
resp = predict(res,x.test=xp)

##check out of sample fit
cat("out of sample cor(f,fhat) is ",cor(fxp,resp$mmean),"\n")
cat("out of sample cor(s,shat) is ",cor(sxp,resp$smean),"\n")

##plot estimated vs. true
##plot the data
plot(xp,yp,cex.axis=1.5,cex.lab=1.5)
lines(xp,fxp,col="blue")
lines(xp,fx+2*sxp,col="blue",lty=2)
lines(xp,fxp-2*sxp,col="blue",lty=2)

## add the fit
lines(xp,resp$mmean) #estimate of f
lines(xp,resp$mmean+2*resp$smean) #estimate of sd
lines(xp,resp$mmean-2*resp$smean) #estimate of sd

rbart documentation built on Aug. 1, 2019, 5:04 p.m.