ExtremalDep (version 1.0.0)

diagnostics: Diagnostics plots for MCMC algorithm

Description

This function displays traceplots of the scaling parameter from the proposal distribution of the adaptive MCMC scheme and the associated acceptance probability.

Usage

diagnostics(mcmc)

Value

A graph of traceplots of the scaling parameter from the proposal distribution of the adaptive MCMC scheme and the associated acceptance probability.

Arguments

mcmc

An output of the fGEV or fExtDep.np function with method = "Bayesian".

Author

Simone Padoan, , https://faculty.unibocconi.it/simonepadoan/; Boris Beranger, , https://www.borisberanger.com; Giulia Marcon,

Details

When mcmc is the output of fGEV, this corresponds to a marginal estimation. In this case, diagnostics displays:

• A trace plot of \(\tau\), the scaling parameter in the multivariate normal proposal, which directly affects the acceptance rate.

• A trace plot of the acceptance probabilities of the proposal parameter values.

When mcmc is the output of fExtDep.np, this corresponds to an estimation of the dependence structure following Algorithm 1 in Beranger et al. (2021).

• If the margins are jointly estimated with the dependence (steps 1 and 2), diagnostics provides trace plots of the corresponding scaling parameters (\(\tau_1, \tau_2\)) and acceptance probabilities.

• For the dependence structure (step 3), a trace plot of the polynomial order \(\kappa\) is displayed, along with the associated acceptance probability.

References

Beranger, B., Padoan, S. A. and Sisson, S. A. (2021). Estimation and uncertainty quantification for extreme quantile regions. Extremes, 24, 349--375.

See Also

fExtDep.np

Examples

##################################################
### Example - Pollution levels in Milan, Italy ###
##################################################

if (FALSE) {

  # Dependence structure only
  data(MilanPollution)

  data <- Milan.winter[, c("NO2", "SO2")] 
  data <- as.matrix(data[complete.cases(data), ])

  # Threshold
  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 = 0.1, nsim = 5e4)
  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 = 0.1, nsim = 5e4)
  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 = 5e4)

  diagnostics(pollut1)

}