corrTG {gcKrig}

Compute the Correlation in Transformed Gaussian Random Fields

Description

This function implements two general methods for computing the correlation function in a transformed Gaussian random field.

Usage

corrTG(marg1, marg2, corrGauss = 0.5, method = "integral", nrep = 1000,
       kmax = 10, earlystop = FALSE, epscut = 1e-3)

Arguments

marg1

an object of class marginal.gc specifying the first marginal distribution.

marg2

an object of class marginal.gc specifying the second marginal distribution.

corrGauss

the correlation in the Gaussian random field. Should be a scalar between 0 and 1.

method

the computation method of calculating correlation in the transformed Gaussian random field. Can be either "integral" or "mc". If use "integral" then a series expansion based on the Hermite Polynomials will be used to approximate the correlation, see De Oliveira (2013) or Han and De Oliveira (2016). If use "mc" then the Monte Carlo method will be used.

nrep

the Monte Carlo size in computing the correlation. Only need to be specified if method = "mc".

kmax

the maximum number of terms used in the series summation (with Hermite polynomial expansion). Only need to be specified if method = "integral".

earlystop

whether or not to allow the series summation to stop early. If earlystop = FALSE then a total number of kmax terms will be kept. If earlystop = TRUE then the series will be automatically truncated if the absolute values of the three consecutive terms are smaller than epscut.

epscut

a small positive value used to truncate the series.

Value

If method = "mc" the output is a scalar between 0 and 1, denoting the correlation of the transformed Gaussian random field. If method = "integral" the output is a scalar of the correlation in the transformed Gaussian random field, and a list of the values in the series expansion based on the integral with Hermite polynomials.

Author(s)

Zifei Han [e-mail]

References

De Oliveira, V. (2013) Hierarchical Poisson models for spatial count data. Journal of Multivariate Analysis,122:393-408.

Han, Z. and De Oliveira, V. (2016) On the correlation structure of Gaussian copula models for geostatistical count data. Australian and New Zealand Journal of Statistics, 58:47-69.

Han, Z. and De Oliveira, V. (2018) gcKrig: An R Package for the Analysis of Geostatistical Count Data Using Gaussian Copulas. Journal of Statistical Software, 87(13), 1–32. doi: 10.18637/jss.v087.i13.

Examples

## Not run: 
corrTG(marg1 = poisson.gc(lambda = 10), marg2 = binomial.gc(size = 1, prob = 0.1),
       corrGauss = 0.5, method = "integral", kmax = 10, earlystop = TRUE, epscut = 1e-5)
set.seed(12345)
corrTG(marg1 = poisson.gc(lambda = 10), marg2 = binomial.gc(size = 1, prob = 0.1),
       corrGauss = 0.5, nrep = 100000, method = "mc")

## End(Not run)