Rejection Sampling

Performs rejection sampling to generate samples from a target distribution. Each draw can come from its own target: draw i is sampled from f evaluated at the i-th element of every per-draw argument in ..., under the envelope max_f[i].

Usage

rejection_sampling(n, f, max_f, proposal_fun, ...)

Arguments

n

Integer. The number of samples to generate.

f

Function. The target density divided by the proposal density, up to a constant; with a uniform proposal, the target density itself. Its first argument takes a vector of proposals, generally not of length n; f must be vectorized over it and over the per-draw arguments in ....

max_f

Numeric. A finite upper bound of f, either a single value or one value per draw (length n). A bound below the maximum of f biases the draws without a warning.

proposal_fun

Function. A function that generates samples from the proposal distribution.

...

Additional arguments to be passed to the target density function f. With n > 1, arguments of length n are taken per draw, so draw i uses their i-th elements. Arguments of any other length are passed whole to every call of f; recycle them with rep_len(x, n) to use them per draw. Pass constants whose length may equal n, such as a lookup table, through the closure of f instead of ....

Value

A numeric vector of length n containing samples from the target distribution.

Examples

target_density <- function(x) brms::dvon_mises(x, mu = 0, kappa = 10)
proposal <- function(n) runif(n, min = -pi, max = pi)
samples <- rejection_sampling(10000, target_density, max_f = target_density(0), proposal)
hist(samples, freq = FALSE)
curve(target_density, col = "red", add = TRUE)


# one location per draw
mu <- rep(c(0, 2), 5000)
samples <- rejection_sampling(
  10000, brms::dvon_mises, max_f = brms::dvon_mises(0, 0, 10), proposal,
  mu = mu, kappa = 10
)
tapply(samples, mu, mean)
#>             0             2 
#> -0.0009627108  1.9951207670