imh_pseudo {qslice}

Independence Metropolis-Hastings

Description

Independence Metropolis-Hastings

Usage

imh_pseudo(x, log_target, pseudo)

Arguments

x

The current state (scalar or numeric vector).

log_target

A function taking a scalar or numeric vector that evaluates the log-target density, returning a numeric scalar.

pseudo

List specifying the pseudo-target (proposal distribution). If the list length is equal to the number of dimensions in x, each element is itself a list that specifies the pseudo-target for the corresponding dimension with functions ld that evaluates the log density for that dimension, and q that evaluates the quantile (inverse-CDF) function for that dimension. If the dimension of x is one, then supply only the inner list specifying the single pseudo-target.

If x is a vector but a single pseudo-target is supplied, the list must contain a log-density function ld that accepts a vector, and a r function that takes no arguments and generates a single multivariate draw from the proposal distribution.

Value

A list containing the new state, x, and whether the proposed value was accepted, logical accpt.

Examples

lf <- function(x) dbeta(x[1], 3, 4, log = TRUE) + dbeta(x[2], 5, 3, log = TRUE)
n_iter <- 100 # set to 1e3 for more complete illustration
draws <- matrix(0.2, nrow = n_iter, ncol = 2)
nAccpt <- 0L
pseudo <- list( list(ld = function(x) dbeta(x, 2, 2, log = TRUE),
                     q = function(u) qbeta(u, 2, 2)),
                list(ld = function(x) dbeta(x, 2, 2, log = TRUE),
                     q = function(u) qbeta(u, 2, 2))
)
for (i in seq.int(2, n_iter)) {
 out <- imh_pseudo(draws[i - 1, ], log_target = lf, pseudo = pseudo)
 draws[i,] <- out$x
 nAccpt <- nAccpt + out$accpt
 cat(i, '\r')
}
nAccpt / (nrow(draws) - 1)
plot(draws[,1], draws[,2], xlim = c(0, 1))
hist(draws[,1], freq = FALSE); curve(dbeta(x, 3, 4), col = "blue", add = TRUE)
hist(draws[,2], freq = FALSE); curve(dbeta(x, 5, 3), col = "blue", add = TRUE)