fExtDep {ExtremalDep} | R Documentation |
Extremal dependence estimation
Description
This function estimates the parameters of extremal dependence models.
Usage
fExtDep(x, method="PPP", model, par.start = NULL,
c = 0, optim.method = "BFGS", trace = 0,
Nsim, Nbin = 0, Hpar, MCpar, seed = NULL)
## S3 method for class 'ExtDep_Freq'
plot(x, type, log=TRUE, contour=TRUE, style, labels,
cex.dat=1, cex.lab=1, cex.cont=1, Q.fix, Q.range,
Q.range0, cond=FALSE,...)
## S3 method for class 'ExtDep_Freq'
logLik(object, ...)
## S3 method for class 'ExtDep_Bayes'
plot(x, type, log=TRUE, contour=TRUE, style, labels,
cex.dat=1, cex.lab=1, cex.cont=1, Q.fix, Q.range,
Q.range0, cond=FALSE, cred.ci=TRUE, subsamp, ...)
## S3 method for class 'ExtDep_Bayes'
summary(object, cred=0.95, plot=FALSE, ...)
Arguments
x |
|
object |
|
method |
A character string indicating the estimation method inlcuding |
model |
A character string with the name of the model. When |
par.start |
A vector representing the initial parameters values for the optimization algorithm. |
c |
A real value in |
optim.method |
A character string indicating the optimization algorithm. Required when |
trace |
A non-negative integer, tracing the progress of the optimization. Required when |
Nsim |
An integer indicating the number of MCMC simulations. Required when |
Nbin |
An integer indicating the length of the burn-in period. Required when |
Hpar |
A list of hyper-parameters. See 'details'. Required when |
MCpar |
A positive real representing the variance of the proposal distirbution. See 'details'. Required when |
seed |
An integer indicating the seed to be set for reproducibility, via the routine |
type |
For |
log |
Required for |
contour |
Required for |
style |
Required for |
labels |
Required for |
cex.dat |
Required for |
cex.lab |
Required for |
cex.cont |
Required for |
Q.fix |
Required for |
Q.range |
Required for |
Q.range0 |
Required for |
cond |
Required for |
cred.ci |
Required for |
subsamp |
Required for |
cred |
A probability indicating the coverage of the credible interval. |
plot |
A logical value. If |
... |
Additional graphical arguments for the |
Details
Regarding the fExtDep.np
function:
When method="PPP"
the approximate likelihood is used to estimate the model parameters. It relies on the dExtDep
function with argument method="Parametric"
and angular=TRUE
.
When method="BayesianPPP"
a Bayesian estimation procedure of the spatral measure is considered, following Sabourin et al. (2013) and Sabourin & Naveau (2014). The argument Hpar
is required to specify the hyper-parameters of the prior distributions, taking the following into consideration:
For the Pairwise Beta model, the parameters components are independent, log-normal. The vector of parameters is of size
choose(dim,2)+1
with positive components. The first elements are the pairiwse dependence parametersb
and the last one is the global dependence parameteralpha
. The list of hyper-parameters should be of the formmean.alpha=, mean.beta=, sd.alpha=, sd.beta=
;For the Husler-Reiss model, the parameters are independent, log-normally distributed. The elements correspond to the
lambda
parameter. The list of hyper-parameters should be of the formmean.lambda=, sd.lambda=
;For the Dirichlet model, the parameters are independent, log-normally distributed. The elements correspond to the
alpha
parameter. The list of hyper-parameters should be of the formmean.alpha=, sd.alpha=
;For the Extremal-t model, the parameters are independent, logit-squared for
rho
and log-normal formu
. The first elements correspond to the correlation parametersrho
and the last parameter is the global dependence parametermu
. The list of hyper-parameters should be of the formmean.rho=, mean.mu=, sd.rho=, sd.mu=
;For the Extremal skewt-t model, the parameters are independent, logit-squared for
rho
, normal foralpha
and log-normal formu
. The first elements correspond to the correlation parametersrho
, then the skewness parametersalpha
and the last parameter is the global dependence parametermu
. The list of hyper-parameters should be of the formmean.rho=, mean.alpha=, mean.mu=, sd.rho=, sd.alpha=, sd.mu=
;For the Asymmetric Logistic model, the parameters' components are independent, log-normal for
alpha
and logit forbeta
. The list of hyper-parameters should be of the formmean.alpha=, mean.beta=, sd.alpha=, sd.beta=
.
The proposal distribution for each (transformed) parameter is a normal distribution centred on the (transformed) current parameter value, with variance MCpar
.
When method="Composite"
, the pairwise composite likelihood is applied, based on the dExtDep
function with argument method="Parametric"
and angular=FALSE
.
Regarding the code plot
method function:
Refer to the angular.plot
, pickands.plot
or returns.plot
functions.
When displaying the bivariate angular density, there is the choice to summarise the data using a histogram (style="hist"
) or to display the observations using tick marks (style="ticks"
).
When displaying the trivariate angular density, the size of the data points can be controlled using cex.dat
.
Value
fExtDep
:
When method == "PPP"
or "Composite"
, a list of class ExtDep_Freq
is returned including
- model:
The argument
model
.- par:
The estimated parameters.
- LL:
The maximised log-likelihood.
- SE:
The standard errors.
- TIC:
The Takeuchi Information Criterion.
- data:
The argument
x
.
When method == "BayesianPPP"
, a list of class ExtDep_Bayes
is returned including
- stored.vales:
A
(Nsim-Nbin)*d
matrix, whered
is the dimension of the parameter space- llh:
A vector of size
(Nsim-Nbin)
containing the log-likelihoods evaluated at each parameter of the posterior sample.- lprior:
A vector of size
(Nsim-Nbin)
containing the logarithm of the prior densities evaluated at each parameter of the posterior sample.- arguments:
The specifics of the algorithm.
- elapsed:
The time elapsed, as given by
proc.time
between the start and end of the run.- Nsim:
The same as the passed argument.
- Nbin:
Idem.
- n.accept:
The total number of accepted proposals.
- n.accept.kept:
The number of accepted proposals after the burn-in period.
- emp.mean:
The estimated posterior parameters mean.
- emp.sd:
The empirical posterior sample standard deviation.
- BIC:
The Bayesian Information Criteria.
logLik:
method function: A numerical value indicating the value of the maximized log-likelihood.
Author(s)
Simone Padoan, simone.padoan@unibocconi.it, https://faculty.unibocconi.it/simonepadoan/; Boris Beranger, borisberanger@gmail.com https://www.borisberanger.com;
References
Beranger, B. and Padoan, S. A. (2015). Extreme dependence models, chapater of the book Extreme Value Modeling and Risk Analysis: Methods and Applications, Chapman Hall/CRC.
Sabourin, A., Naveau, P. and Fougeres, A-L (2013) Bayesian model averaging for multivariate extremes Extremes, 16, 325-350.
Sabourin, A. and Naveau, P. (2014) Bayesian Dirichlet mixture model for multivariate extremes: A re-parametrization Computational Statistics & Data Analysis, 71, 542-567.
See Also
dExtDep
, pExtDep
, rExtDep
, fExtDep.np
Examples
# Example using the Poisson Point Proce Process appraoch
data(pollution)
f.hr <- fExtDep(x=PNS, method="PPP", model="HR",
par.start = rep(0.5, 3), trace=2)
plot(x=f.hr, type="angular",
labels=c(expression(PM[10]), expression(NO), expression(SO[2])),
cex.lab=2)
plot(x=f.hr, type="pickands",
labels=c(expression(PM[10]), expression(NO), expression(SO[2])),
cex.lab=2) # Takes time!
# Example using the pairwise composite (full) likelihood
set.seed(1)
data <- rExtDep(n=300, model="ET", par=c(0.6,3))
f.et <- fExtDep(x=data, method="Composite", model="ET",
par.start = c(0.5, 1), trace=2)
plot(x=f.et, type="angular", cex.lab=2)