Calculate posterior mean vector and covariance matrix

Usage

GP(
  x,
  xprime,
  y,
  covfun,
  noise = 0,
  optim = FALSE,
  method = c("L-BFGS-B", "Nelder-Mead", "BFGS", "CG", "SANN", "Brent"),
  ...
)

Arguments

x: numeric vector of input data
xprime: numeric vector of data points to predict
y: numeric vector of values to learn from
covfun: function specifying the covariance function to use
noise: numeric scalar denoting the noise variance to add to the (x, x) covariance matrix of observations. Defaults to 0 for no noise modelling
optim: Boolean whether to optimise hyperparameters using negative marginal log likelihood. Defaults to FALSE
method: character denoting the optimisation algorithm in stats::optim to use if optim = TRUE. Defaults to "L-BFGS-B"
...: covariance function hyperparameters to be passed to the covariance functions within cov_function

Value

TSGP object containing the input data, posterior mean function and covariance matrix

Author

Trent Henderson

Examples

x1 <- 1:100

y <- 3 * sin(2 * seq(0, 4 * pi, length.out = 100)) +
  runif(100) * 2 + (0.08 * seq(from = 1, to = 100, by = 1))

CovSum <- function(xa, xb, sigma_1 = 1, sigma_2 = 1, l_1 = 1, l_2 = 1, p = 1){
  Sigma_exp_quad <- cov_exp_quad(xa, xb, sigma_1, l_1)
  Sigma_periodic <- cov_periodic(xa, xb, sigma_2, l_2, p)
  X <- Sigma_exp_quad + Sigma_periodic
  X <- structure(X, class = c("GPCov", "matrix"))
  return(X)
}

mod <- GP(x1, 1:length(y), y, CovSum, 0.8,
          sigma_1 = 5, sigma_2 = 1,
          l_1 = 75, l_2 = 1, p = 25)