Condition a Gaussian Process

Condition a Multivariate Normal distribution based on a Gaussian Process using a exponentiated quadratic covariance matrix.

Usage

condition_gaussian_process(
  n,
  x,
  y,
  x_new,
  amplitude = 1,
  length_scale = 1,
  delta = 1e-09
)

Arguments

n

number of random draws.

x

position of values to condition on.

y

values to condition on (at positions x).

x_new

new positions to estimate values at.

amplitude

Vertical scale of the covariance function

length_scale

Horizontal scale of the covariance function

delta

A small offset along the diagonal of the resulting covariance matrix to ensure the function returns a positive-semidefinite matrix. Can also be used as a white noise kernel to allow for increased variation at individual positions along the vector x.

Value

A matrix of size \(M \times N\), where \(M\) is length(x_new), and \(N\) is n. Each column is a random draw from the conditioned multivariate normal where each row corresponds to the draw at the position in x_new.

Examples

x <- 1:10
y <- rep(0, 10)
x_new <- 11:15

condition_gaussian_process(3, x, y, x_new)
#>             [,1]      [,2]      [,3]
#> [1,]  0.19929390 0.5272291 0.5268134
#> [2,] -1.33092476 0.4944712 0.2263466
#> [3,] -2.58605557 0.7990859 2.0358786
#> [4,] -0.42659913 0.5567059 2.4631173
#> [5,]  0.06881175 0.9354856 0.4857316