View source: R/plot_ExpDep.np.R
summary_ExtDep | R Documentation |
This function computes summaries on the posterior sample obtained from the adaptive MCMC scheme for the non-parametric estimation of a bivariate dependence structure.
summary_ExtDep(object, mcmc, burn, cred=0.95, plot=FALSE, ...)
object |
A vector of values on [0,1]. If missing, a regular grid of length 100 is considered. |
mcmc |
An output of the |
burn |
A positive integer indicating the burn-in period. |
cred |
A value in [0,1] indicating the level of the credibility intervals to be computed. |
plot |
A logical value; if |
... |
Additional graphical parameters for |
For each value say ω \in [0,1] given, the complement 1-ω is automatically computed to define the observation (ω,1-ω) 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
.
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 κ;
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 (η parametrisation);
beta_post
: Posterior sample for the Bernstein polynomial coefficients (β parametrisation);
p0_post
, p1_post
: Posterior sample for point masses p_0 and p_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;
Simone Padoan, simone.padoan@unibocconi.it, https://faculty.unibocconi.it/simonepadoan/; Boris Beranger, borisberanger@gmail.com https://www.borisberanger.com
fExtDep.np
.
#################################################### ### Example - Pollution levels in Milan, Italy ### #################################################### if(interactive()){ ### 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) }
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