summary_ExtDep {ExtremalDep} | R Documentation |
Summary of MCMC algorithm.
Description
This function computes summaries on the posterior sample obtained from the adaptive MCMC scheme for the non-parametric estimation of a bivariate dependence structure.
Usage
summary_ExtDep(object, mcmc, burn, cred=0.95, plot=FALSE, ...)
Arguments
object |
A vector of values on |
mcmc |
An output of the |
burn |
A positive integer indicating the burn-in period. |
cred |
A value in |
plot |
A logical value; if |
... |
Additional graphical parameters for |
Details
For each value say given, the complement
is automatically computed to define the observation
on the bivariate unit simplex.
It is obvious that the value of burn
must be greater than the number of iterations in the mcmc algorithm. This can be found in mcmc
.
Value
The function returns a list with the following objects:
k.median
,k.up
,k.low
: Posterior median, upper and lower bounds of the CI for the estimated Bernstein polynomial degree;
h.mean
,h.up
,h.low
: Posterior mean, upper and lower bounds of the CI for the estimated angular density;
A.mean
,A.up
,A.low
: Posterior mean, upper and lower bounds of the CI for the estimated Pickands dependence function;
p0.mean
,p0.up
,p0.low
: Posterior mean, upper and lower bounds of the CI for the estimated point mass;
p1.mean
,p1.up
,p1.low
: Posterior mean, upper and lower bounds of the CI for the estimated point mass;
A_post
: Posterior sample for Pickands dependence function;h_post
: Posterior sample for angular density;eta.diff_post
: Posterior sample for the Bernstein polynomial coefficients (parametrisation);
beta_post
: Posterior sample for the Bernstein polynomial coefficients (parametrisation);
p0_post
,p1_post
: Posterior sample for point massesand
;
w
: A vector of values on the bivariate simplex where the angular density and Pickands dependence function were evaluated;burn
: The argument provided;
If the margins were also fitted, the list given as object
would contain mar1
and mar2
and the function would also output:
mar1.mean
,mar1.up
,mar1.low
: Posterior mean, upper and lower bounds of the CI for the estimated marginal parameter on the first component;mar2.mean
,mar2.up
,mar2.low
: Posterior mean, upper and lower bounds of the CI for the estimated marginal parameter on the second component;mar1_post
: Posterior sample for the estimated marginal parameter on the first component;mar2_post
: Posterior sample for the estimated marginal parameter on the second component;
Author(s)
Simone Padoan, simone.padoan@unibocconi.it, https://faculty.unibocconi.it/simonepadoan/; Boris Beranger, borisberanger@gmail.com https://www.borisberanger.com
See Also
Examples
####################################################
### Example - Pollution levels in Milan, Italy ###
####################################################
## Not run:
### Here we will only model the dependence structure
data(MilanPollution)
data <- Milan.winter[,c("NO2","SO2")]
data <- as.matrix(data[complete.cases(data),])
# Thereshold
u <- apply(data, 2, function(x) quantile(x, prob=0.9, type=3))
# Hyperparameters
hyperparam <- list(mu.nbinom = 6, var.nbinom = 8, a.unif=0, b.unif=0.2)
### Standardise data to univariate Frechet margins
f1 <- fGEV(data=data[,1], method="Bayesian", sig0 = 0.0001, nsim = 5e+4)
diagnostics(f1)
burn1 <- 1:30000
gev.pars1 <- apply(f1$param_post[-burn1,],2,mean)
sdata1 <- trans2UFrechet(data=data[,1], pars=gev.pars1, type="GEV")
f2 <- fGEV(data=data[,2], method="Bayesian", sig0 = 0.0001, nsim = 5e+4)
diagnostics(f2)
burn2 <- 1:30000
gev.pars2 <- apply(f2$param_post[-burn2,],2,mean)
sdata2 <- trans2UFrechet(data=data[,2], pars=gev.pars2, type="GEV")
sdata <- cbind(sdata1,sdata2)
### Bayesian estimation using Bernstein polynomials
pollut1 <- fExtDep.np(method="Bayesian", data=sdata, u=TRUE,
mar.fit=FALSE, k0=5, hyperparam = hyperparam, nsim=5e+4)
diagnostics(pollut1)
pollut1_sum <- summary_ExtDep(mcmc=pollut1, burn=3e+4, plot=TRUE)
## End(Not run)