gpr: Gaussian Process regression for single curve

Description

Gaussian Process regression for single curve with train data.

Usage

gpr(Data, response, Cov, hyper=NULL, NewHyper=NULL, mean=0, gamma=1)

Arguments

Data

The input data from train data.

hyper

The hyper parameters. Must be a list.

NewHyper

Vector of the names of the new hyper parameters from customized kernel function.

mean

Is the mean taken out when analysis? Default to be 0, which assumes the mean is zero. if assume mean is a constant, mean=1; if assume mean is a linear trend, mean='t'.

response

The response data from train data.

Cov

The kernel functions or covariance functions to use.

gamma

Power parameter used in powered exponential kernel function.

Value

CovFunCovariance function type
fittedFitted value of training data
fitted.sdStandard deviation of the fitted value of training data
gammaParameter used in powered exponential covariance function
hyperHyper-parameter estimated from training data
IVariance of the estimated hyper-parameters
train.xTraining covariates
train.yTraining response
QCovariance matrix
invInverse of the covariance matrix
meanThe mean assumed in the analysis
lrm'lm' object if mean is a linear regression. NULL otherwise.

References

Shi, J Q., and Choi, T. (2011), Gaussian Process Regression Analysis for Functional Data, Springer, New York.

Examples

Run this code

library(GPFDA)
library(MASS) ## used to generate data
hp <- list('pow.ex.w'=log(10),'linear.a'=log(10),'pow.ex.v'=log(5),'vv'=log(1))
c <- seq(0,1,len=40)
idx <- sort(sample(1:40,21))
X <- as.matrix(c[idx])
Y <- (mvrnorm(n=40,mu=c-c,Sigma=(cov.linear(hp,c)+cov.pow.ex(hp,c)))[1,])+sin(c*6)
Y <- as.matrix(Y[idx])
x <- as.matrix(seq(0,1,by=0.03))
a <- gpr(X,Y,c('linear','pow.ex'))