| AdMitMH {AdMit} | R Documentation |
Performs independence chain Metropolis-Hastings (M-H) sampling using an adaptive mixture of Student-t distributions as the candidate density
AdMitMH(N=1e5, KERNEL, mit=list(), ...)
N |
number of draws generated by the independence chain M-H algorithm (positive
integer number). Default: N=1e5. |
KERNEL |
kernel function of the target density on which the adaptive mixture is fitted. This
function should be vectorized for speed purposes (i.e., its first
argument should be a matrix and its output a vector). Moreover, the function must contain
the logical argument log. If log=TRUE, the function
returns (natural) logarithm values of kernel function. NA
and NaN values are not allowed. |
mit |
list containing information on the mixture approximation (see *Details*). |
... |
further arguments to be passed to KERNEL. |
The argument mit is a list containing information on the
adaptive mixture of Student-t distributions. The following components must
be provided:
pmuSigmadf
where H (>=1) is the number of components and
d (>=1) is the dimension of the first argument in KERNEL. Typically,
mit is estimated by the function AdMit.
A list with the following components:
draws: matrix (of size Nxd) of draws
generated by the independence chain M-H algorithm,
where N (>=1) is the number of draws
and d (>=1) is the
dimension of the first argument in KERNEL.
accept: acceptance rate of the independence chain M-H algorithm.
Further details and examples of the R package AdMit
can be found in Ardia, Hoogerheide and van Dijk (2008). http://www.tinbergen.nl/
Further information on the Metropolis-Hastings algorithm can be found in Chib and Greenberg (1995) and Koop (2003).
David Ardia <david.ardia@unifr.ch>
Ardia, D., Hoogerheide, L.F., van Dijk, H.K. (2008) `Adaptive mixture of Student-t distributions as a flexible candidate distribution for efficient simulation: The R package AdMit', Working paper, Econometric Institute, Erasmus University Rotterdam (NL). URLLINK
Chib, S., Greenberg, E. (1995) `Understanding the Metropolis-Hasting Algorithm', The American Statistician 49(4), pp.327–335.
Koop, G. (2003) Bayesian Econometrics, Wiley-Interscience (London, UK), first edition, ISBN: 0470845678.
AdMitIS for importance sampling using an adaptive
mixture of Student-t distributions as the importance density,
AdMit for fitting
an adaptive mixture of Student-t distributions to a target density
through its KERNEL function; the package coda for MCMC output
analysis (the package is loaded automatically with the package AdMit).
## Gelman and Meng (2001) kernel function
'GelmanMeng' <- function(x, A=1, B=0, C1=3, C2=3, log=TRUE)
{
if (is.vector(x))
x <- matrix(x, nrow=1)
r <- -.5 * (A*x[,1]^2*x[,2]^2 + x[,1]^2 + x[,2]^2
- 2*B*x[,1]*x[,2] - 2*C1*x[,1] - 2*C2*x[,2])
if (!log)
r <- exp(r)
as.vector(r)
}
## Run the AdMit function to fit the mixture approximation
set.seed(1234)
outAdMit <- AdMit(GelmanMeng, mu0=c(0,0.1))
## Run M-H using the mixture approximation as the candidate density
outAdMitMH <- AdMitMH(KERNEL=GelmanMeng, mit=outAdMit$mit)
options(digits=4, max.print=40)
print(outAdMitMH)
## Use functions provided by the package coda to obtain
## quantities of interest for the density whose kernel is 'GelmanMeng'
draws <- as.mcmc(outAdMitMH$draws[1001:1e5,])
colnames(draws) <- c("X1","X2")
summary(draws)
summary(draws)$stat[,3]^2 / summary(draws)$stat[,4]^2 ## RNE
plot(draws)