summary.bbeed: Compute summary statistics from the MCMC output.

Description

Summary statistics of the MCMC output obtained from the Bayesian method based on the Bernstein polynomials for inferring the angular measure and Pickands dependence functions.

Usage

# S3 method for bbeed
summary(object, mcmc, burn, conf=0.95, plot=FALSE, ...)

Arguments

object

The values (on the simplex) at which the dependence is evaluated

mcmc

The output of an MCMC algorithm given by beed

burn

The burn-in period

conf

The confidence region

plot

If plot=TRUE then the function plot.beed is used.

...

Arguments to be passed for the graphical parameters

Value

Returns a list that contains: * the conf-, 0.5- and 1-conf-quantiles and posterior sample for k (the polynomial order), * the conf- and 1-conf-quantiles, mean and posterior sample for h (the angular density), A (the Pickands dependence function), p0 and p1 (the point masses at the endpoints of the simplex), mar1 and mar2 (the marginal parameters, if they exist). To access them, the names are for example k.low, k.median, k.up and k_post. * w and burn which are the inputs object and burn.

References

Marcon G., Padoan, S.A. and Antoniano-Villalobos I. (2016) Bayesian Inference for the Extremal Dependence. Electronic Journal of Statistics, 10.2, 3310-3337.

Examples

Run this code

# NOT RUN {
# This reproduces some of the results showed in Fig. 1 (Marcon, 2016).
set.seed(1890)
data <- evd::rbvevd(n=100, dep=.6, asy=c(0.8,0.3), model="alog", mar1=c(1,1,1))

nsim = 500000
burn = 400000

mu.nbinom = 3.2
var.nbinom = 4.48
hyperparam <- list(a.unif=0, b.unif=.5, mu.nbinom=mu.nbinom, var.nbinom=var.nbinom)
k0 = 5
pm0 = list(p0=0.06573614, p1=0.3752118)
eta0 = ExtremalDep:::rcoef(k0, pm0)

mcmc <- bbeed(data, pm0, eta0, k0, hyperparam, nsim,
              prior.k = "nbinom", prior.pm = "unif")

w <- seq(0.001, .999, length=100)
summary.mcmc <- summary.bbeed(w, mcmc, burn, nsim, plot=TRUE)
# }