Description Usage Arguments Details Value Warning Author(s) References See Also Examples
View source: R/condSimMaxStab.R
This function performs conditional simulation of various max-stable processes.
1 2 | condrmaxstab(k = 1, coord, cond.coord, cond.data, cov.mod = "powexp",
..., do.sim = TRUE, thin = n.cond, burnin = 50, parts)
|
k |
An integer. The number of conditional simulations to be generated. |
coord |
A vector or matrix that gives the coordinates of each location. Each row corresponds to one location - if any. |
cond.coord |
A vector or matrix that gives the coordinates of each conditional location. Each row corresponds to one location - if any. |
cond.data |
A vector that gives the conditional values at the corresponding conditioning locations. Each row corresponds to one location - if any. |
cov.mod |
A character string that gives the max-stable model. This must be one of "brown" for the Brown-Resnick model, or "whitmat", "cauchy", "powexp" and "bessel" for the Schlather model with the given correlation family. |
... |
The parameters of the max-stable model. See
|
do.sim |
A logical value. If |
thin |
A positive integer giving by which amount the generated Markov chain should be thinned. This is only useful when the number of conditioning locations is greater than 7. |
burnin |
A positive integer giving the duration of the burnin period of the Markov chain. |
parts |
A matrix giving the hitting scenarios. Each row corresponds to one hitting scenarios. If missing then a Gibbs sampler will be used to generate such hitting scenarios. |
The algorithm consists in three steps:
Draw a random partition θ from
Pr{θ = τ | Z(x) = z}
Given the random partition, draw the extremal functions from
Pr{φ^+ in . | Z(x) = z, θ = τ}
Independently, draw the sub-extremal functions, i.e.,
max_{i ≥q 1} φ_i 1_{φ_i(x) < z}.
The distribution in Step 1 is usually intractable and in such cases a random scan Gibbs sampler will be used to sample from this distribution.
This function returns a list whose components are
sim |
The conditional simulations. Beware the first values corresponds to the conditioning values. |
sub.ext.fct |
The values of the sub-extremal functions. |
ext.fct |
The values of the extremal functions. |
timings |
The timings in seconds for each step of the algorithm. |
This function can be extremely time consuming when the number of conditioning locations is large.
Mathieu Ribatet
Dombry, C. and Eyi-Minko, F. (2012) Regular conditional distributions of max infinitely divisible processes. Submitted.
Dombry, C., Eyi-Minko, F. and Ribatet, M. (2012) Conditional simulation of max-stable processes. To appear in Biometrika.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 | n.sim <- 50
n.cond <- 5
range <- 10
smooth <- 1.5
n.site <- 200
coord <- seq(-5, 5, length = n.site)
cond.coord <- seq(-4, 4, length = n.cond)
all.coord <- c(cond.coord, coord)
all.cond.data <- rmaxstab(1, all.coord, "powexp", nugget = 0, range = range,
smooth = smooth)
cond.data <- all.cond.data[1:n.cond]
ans <- condrmaxstab(n.sim, coord, cond.coord, cond.data, range = range,
smooth = smooth, cov.mod = "powexp")
idx <- order(all.coord)
matplot(coord, t(log(ans$sim)), type = "l", col = "grey", lty = 1,
xlab = expression(x), ylab = expression(Z(x)))
lines(all.coord[idx], log(all.cond.data)[idx])
points(cond.coord, log(cond.data), pch = 15, col = 2)
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