sk_sim {snapKrig}

Random draw from multivariate normal distribution for sk grids

Description

Generates a random draw from the multivariate Gaussian distribution for the covariance model pars on grid g, with mean zero.

Usage

sk_sim(g, pars = sk_pars(g), n_layer = 1, fac = NULL, sk_out = TRUE)

Arguments

g

an sk object or any grid object accepted by sk

pars

list, covariance parameters in form returned by sk_pars

n_layer

positive integer, the number of draws to return

fac

list, optional pre-computed factorization of component correlation matrices

sk_out

logical, if TRUE an sk grid is returned

Details

pars and g define the model's covariance matrix V. This function uses base::rnorm to get a vector of independent standard normal variates, which it multiplies by the square root of the covariance matrix, V, for the desired model (as defined by pars and g). The result has a multivariate normal distribution with mean zero and covariance V.

Multiple independent draws can be computed more efficiently by reusing the factorization of V. This can be pre-computed with sk_var and supplied in fac, or users can set n_layer and the function will do this automatically.

Value

sk grid or its vectorized form (vector for single-layer case, matrix for multi-layer case)

See Also

sk sk_pars base::rnorm

Other variance-related functions: sk_GLS(), sk_LL(), sk_cmean(), sk_nLL(), sk_var()

Examples

# example grid and covariance parameters
gdim = c(100, 200)
g = sk(gdim)
pars_gau = sk_pars(g)

# this example has a large nugget effect
g_sim = sk_sim(g, pars_gau)
plot(g_sim)

# repeat with smaller nugget effect for less noisy data
pars_smooth = utils::modifyList(pars_gau, list(eps=1e-2))
g_sim = sk_sim(g, pars_smooth)
plot(g_sim)

# the nugget effect can be very small, but users should avoid eps=0
pars_smoother = utils::modifyList(pars_gau, list(eps=1e-12))
g_sim = sk_sim(g, pars_smoother)
plot(g_sim)

# multi-layer example
g_sim_multi = sk_sim(g, pars_smoother, n_layer=3)
plot(g_sim_multi, layer=1)
plot(g_sim_multi, layer=2)
plot(g_sim_multi, layer=3)