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 \omega \in [0,1]
given, the complement 1-\omega
is automatically computed to define the observation (\omega,1-\omega)
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
\kappa
;- h.mean, h.up, h.low:
Posterior mean, upper and lower bounds of the CI for the estimated angular density
h
;- A.mean, A.up, A.low:
Posterior mean, upper and lower bounds of the CI for the estimated Pickands dependence function
A
;- p0.mean, p0.up, p0.low:
Posterior mean, upper and lower bounds of the CI for the estimated point mass
p_0
;- p1.mean, p1.up, p1.low:
Posterior mean, upper and lower bounds of the CI for the estimated point mass
p_1
;- 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 (
\eta
parametrisation);- beta_post:
Posterior sample for the Bernstein polynomial coefficients (
\beta
parametrisation);- p0_post, p1_post:
Posterior sample for point masses
p_0
andp_1
;- 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)