`WarpKriging::update_simulate`

Description

Update previous simulation of a WarpKriging model object.

This method draws paths of the stochastic process conditional on the values at the input points used in the fit, plus the new input points and their values given as argument (known as ‘update’ points).

Usage

Python

# wk = WarpKriging(...)
# wk.simulate(nsim = 1, seed = 123, x, will_update = True)
wk.update_simulate(y_u, X_u)

R

# wk <- WarpKriging(...)
# wk$simulate(nsim = 1, seed = 123, x, will_update = TRUE)
wk$update_simulate(y_u, X_u)

Matlab/Octave

% wk = WarpKriging(...)
% wk.simulate(nsim = 1, seed = 123, x, will_update = true)
wk.update_simulate(y_u, X_u)

Julia

# wk = WarpKriging(...)
# simulate(wk, nsim=1, seed=123, x, will_update=true)
update_simulate(wk, y_u, X_u)

Arguments

Argument	Description
`y_u`	Numeric vector of new responses (output).
`X_u`	Numeric matrix of new input points.

Details

This method updates previously simulated paths after conditioning on the additional observations. The model must first have been simulated with will_update = TRUE.

Value

A matrix with nrow(x) rows and nsim columns containing the updated simulated paths at the input points given in x.

Examples

f <- function(x) 1 - 1 / 2 * (sin(12 * x) / (1 + x) + 2 * cos(7 * x) * x^5 + 0.7)
X <- as.matrix(seq(0.05, 0.95, length.out = 10))
y <- f(X)

wk <- WarpKriging(
  y, X,
  warping = "kumaraswamy",
  kernel = "gauss",
  parameters = list(max_iter_adam = "20", max_iter_bfgs = "10")
)
x <- as.matrix(seq(0, 1, length.out = 101))
s <- wk$simulate(nsim = 10, seed = 123, x = x, will_update = TRUE)

X_u <- as.matrix(c(0.15, 0.85))
y_u <- f(X_u)
s_u <- wk$update_simulate(y_u, X_u)
cat("Updated simulation size:", dim(s_u), "\n")

plot(f)
points(X, y, col = "blue")
points(X_u, y_u, col = "red", pch = 16)
matlines(x, s, col = rgb(0, 0, 1, 0.15), type = "l", lty = 1)
matlines(x, s_u, col = rgb(1, 0, 0, 0.15), type = "l", lty = 1)

Results

Updated simulation size: 101 10 

WarpKriging::update_simulate