evdbayes (version 1.1-3)

Accept Rate: Compute Suited Proposal Standard Deviations

Description

Compute suited proposal standard deviations for the MCMC algorithm.

Usage

ar.choice(init, prior, lh = c("none","gev","gpd","pp","os"), ..., psd,
ar = rep(.4, npar), n = 1000, tol = rep(.05, npar))

Value

Return a list with two arguments. ``psd'': the suited proposal standard deviations and ``ar'': the accept rates related to these proposal standard deviations.

Arguments

init

a numeric vector for the starting value of the MCMC algorithm.

prior

A prior model. See function prior.prob, prior.quant, prior.norm and prior.loglognorm.

lh

The likelihood function. Should be one of ``none'', ``gev'', ``gpd'', ``pp'' and ``os''.

...

Optional arguments to be passed to the posterior function.

psd

The initials proposal standard deviations.

ar

Optional. The objective accept rates - default is rep(.4, npar).

n

Optional. The length of the simulated Markov Chains.

tol

Optional. The tolerance for the convergence test.

Author

Mathieu Ribatet

Details

The suited proposal standard deviations (psd) are computed through trial and error processes. Proposal standard deviations are fundamental to ensure good mixing properties for the Markov Chains.

For this purpose, there exits a thumb rule: ``In small dimensions, aim at an average acceptance rate of 50. In large dimensions, at an average acceptance rate of 25. (Gelman et al., 1995)''.

For numerical conveniences, the trial and error process is more accurate with small initial starting psd.

References

Gelman, A. and Roberts, G. and Gilks, W. (1995) Efficient Metropolis Jumping Rules. Oxford University Press.

Examples

data(rainfall)
prrain <- prior.quant(shape = c(38.9, 7.1, 47), scale = c(1.5, 6.3,
  2.6))
n <- 10000; t0 <- c(43.2, 7.64, 0.32);
s <- ar.choice(init = t0, prior = prrain, lh = "pp", data = rainfall,
  thresh = 40, noy = 54, psd = rep(0.01, 3))