R: Conditional simulation of max-stable processes

condrmaxstab {SpatialExtremes} | R Documentation

## Conditional simulation of max-stable processes

### Description

This function performs conditional simulation of various max-stable processes.

### Usage

    condrmaxstab(k = 1, coord, cond.coord, cond.data, cov.mod = "powexp",
    ..., do.sim = TRUE, thin = n.cond, burnin = 50, parts)

### Arguments

`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 `rmaxstab` for more details.
`do.sim` | A logical value. If `TRUE` (the default), the conditional simulations are performed; otherwise only the simulated random partitions, i.e., the hitting scenarios, are returned.
`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.

### Details

The algorithm consists in three steps:

1. Draw a random partition θ from

   Pr{θ = τ | Z(x) = z}

2. Given the random partition, draw the extremal functions from

   Pr{φ^+ in . | Z(x) = z, θ = τ}

3. 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.

### Value

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.

### Warning

This function can be extremely time consuming when the number of conditioning locations is large.

### Author(s)

Mathieu Ribatet

### References

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.

### See Also

`rmaxstab`, `condrgp`

### Examples

    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)

[Package SpatialExtremes version 2.0-5 Index]