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: |
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 |
mit |
list containing information on the mixture approximation (see *Details*). |
... |
further arguments to be passed to |
The argument mit
is a list containing information on the
adaptive mixture of Student-t distributions. The following components must
be provided:
p
vector (of length H) of mixing probabilities.
mu
matrix (of size Hxd) containing the vectors of modes (in row) of the mixture components.
Sigma
matrix (of size Hxd*d) containing the scale matrices (in row) of the mixture components.
df
degrees of freedom parameter of the Student-t components (real number not smaller than one).
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 N
xd) 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 (2009a,b). See also
the package vignette by typing vignette("AdMit")
.
Further information on the Metropolis-Hastings algorithm can be found in Chib and Greenberg (1995) and Koop (2003).
Please cite the package in publications. Use citation("AdMit")
.
David Ardia
Ardia, D., Hoogerheide, L.F., van Dijk, H.K. (2009a). AdMit: Adaptive Mixture of Student-t Distributions. The R Journal 1(1), pp.25-30. https://journal.R-project.org/archive/2009-1/
Ardia, D., Hoogerheide, L.F., van Dijk, H.K. (2009b). Adaptive Mixture of Student-t Distributions as a Flexible Candidate Distribution for Efficient Simulation: The R Package AdMit. Journal of Statistical Software 29(3), pp.1-32. doi: 10.18637/jss.v029.i03
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). 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.
## NB : Low number of draws for speedup. Consider using more draws! ## Gelman and Meng (1991) 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(KERNEL = GelmanMeng, mu0 = c(0.0, 0.1), control = list(Ns = 1e4)) ## Run M-H using the mixture approximation as the candidate density outAdMitMH <- AdMitMH(N = 1e4, KERNEL = GelmanMeng, mit = outAdMit$mit) options(digits = 4, max.print = 40) print(outAdMitMH) ## Use functions provided by the package coda to obtain ## quantities of interest for the density whose kernel is 'GelmanMeng' library("coda") draws <- as.mcmc(outAdMitMH$draws) draws <- window(draws, start = 1001) colnames(draws) <- c("X1", "X2") summary(draws) summary(draws)$stat[,3]^2 / summary(draws)$stat[,4]^2 ## RNE plot(draws)