MH_mcmc.own: Metropolis-Hastings algorithm for GEV
In proto4426/PissoortThesis: Thesis in Extreme Value Theory

Description Usage Arguments Value Author(s) Examples

When the parameter start is of length 2, the computations are automaically made for a Gumbel model.

1 2	MH_mcmc.own(start, varmat.prop, data = max_years$data, iter = 2000, burnin = ceiling(iter/2 + 1))

`start`	numeric vector of length 3 containing the starting values for the parameters theta= (location, LOG-scale and shape). It is advised explore different ones, and typically take the MPLE
`varmat.prop`	The proposal's variance : controlling the cceptance rate. To facilitate convergence, it is advised to target an acceptance rate of around 0.25 when all components of theta are updated simultaneously, and 0.40 when the components are updated one at a time.
`data`	numeric vector containing the GEV in block-maxima
`iter`	The number of iterations of the algorithm. Must e high enough to ensure convergence

A named list containing

mean.acc_rates : the mean of the acceptance rates
out.chain : The generated chain

Antoine Pissoort, antoine.pissoort@student.uclouvain.be

data("max_years")
fn <- function(par, data) -log_post0(par[1], par[2], par[3], data)
param <- c(mean(max_years$df$Max),log(sd(max_years$df$Max)), 0.1 )
# opt <- optim(param, fn, data = max_years$data,
#              method="BFGS", hessian = TRUE)
opt <- nlm(fn, param, data = max_years$data,
           hessian=T, iterlim = 1e5)
start <- opt$estimate
Sig <- solve(opt$hessian)
ev <- eigen( (2.4/sqrt(2))^2 * Sig)
varmat <- ev$vectors %*% diag(sqrt(ev$values)) %*% t(ev$vectors)
# (MH)
set.seed(100)
mh.mcmc1 <- MH_mcmc.own(start, varmat %*% c(.1,.3,.4))