arms {armspp}  R Documentation 
This function performs Adaptive Rejection Metropolis Sampling to sample from
a target distribution specified by its (potentially unnormalised) log
density. The function constructs a rejection distribution based on piecewise
linear functions that envelop the log density of the target.
If the target is logconcave, the metropolis
parameter can be set to
FALSE
, and an acceptreject sampling scheme is used which yields
independent samples.
Otherwise, if metropolis
is TRUE
, a MetropolisHastings step is
used to construct a Markov chain with a stationary distribution matching the
target. It is possible in this case for the rejection distribution to be a
poor proposal, so users should be careful to check the output matches the
desired distribution.
All arguments other than n_samples
, include_n_evaluations
and
arguments
can be either vectors or lists as appropriate. If they are
vectors, they will be recycled in the same manner as, e.g., rnorm. The
entries of arguments
may be vectors/lists and will also be recycled
(see examples).
arms(n_samples, log_pdf, lower, upper, previous = (upper + lower)/2, initial = lower + (1:n_initial) * (upper  lower)/(n_initial + 1), n_initial = 10, convex = 0, max_points = max(2 * n_initial + 1, 100), metropolis = TRUE, include_n_evaluations = FALSE, arguments = list())
n_samples 
Number of samples to return. 
log_pdf 
Potentially unnormalised log density of target distribution. Can also be a list of functions. 
lower 
Lower bound of the support of the target distribution. 
upper 
Upper bound of the support of the target distribution. 
previous 
The previous value of the Markov chain to be used if

initial 
Initial points with which to build the rejection distribution. 
n_initial 
Number of points used to form 
convex 
Convexity adjustment. 
max_points 
Maximum number of points to allow in the rejection distribution. 
metropolis 
Whether to use a MetropolisHastings step after rejection sampling. Not necessary if the target distribution is log concave. 
include_n_evaluations 
Whether to return an object specifying the number of function evaluations used. 
arguments 
List of additional arguments to be passed to log_pdf 
Vector or matrix of samples if include_n_evaluations
is
FALSE
, otherwise a list.
Gilks, W. R., Best, N. G. and Tan, K. K. C. (1995) Adaptive rejection Metropolis sampling. Applied Statistics, 44, 455472.
http://www1.maths.leeds.ac.uk/~wally.gilks/adaptive.rejection/web_page/Welcome.html
# The normal distribution, which is log concave, so metropolis can be FALSE result < arms( 1000, dnorm, 1000, 1000, metropolis = FALSE, arguments = list(log = TRUE), include_n_evaluations = TRUE ) print(result$n_evaluations) hist(result$samples, freq = FALSE, br = 20) curve(dnorm(x), min(result$samples), max(result$samples), col = 'red', add = TRUE) # Mixture of normals: 0.4 N(1, 1) + 0.6 N(4, 1). Not log concave. dnormmixture < function(x) { parts < log(c(0.4, 0.6)) + dnorm(x, mean = c(1, 4), log = TRUE) log(sum(exp(parts  max(parts)))) + max(parts) } samples < arms(1000, dnormmixture, 1000, 1000) hist(samples, freq = FALSE) # List of log pdfs, demonstrating recycling of log_pdf argument samples < arms( 10, list( function(x) x ^ 2 / 2, function(x) (x  10) ^ 2 / 2 ), 1000, 1000 ) print(samples) # Another way to achieve the above, this time with recycling in arguments samples < arms( 10, dnorm, 1000, 1000, arguments = list( mean = c(0, 10), sd = 1, log = TRUE ) ) print(samples)