  Monte Carlo methods are often necessary for the implementation of optimal
Bayesian estimators. A fundamental technique that can be used to generate
samples from virtually any target probability distribution is the so-called
rejection sampling method, which generates candidate samples from a proposal
distribution and then accepts them or not by testing the ratio of the target
and proposal densities. The class of adaptive rejection sampling (ARS)
algorithms is particularly interesting because they can achieve high acceptance
rates. However, the standard ARS method can only be used with log-concave
target densities. For this reason, many generalizations have been proposed.
  In this work, we investigate two different adaptive schemes that can be used
to draw exactly from a large family of univariate probability density functions
(pdf's), not necessarily log-concave, possibly multimodal and with tails of
arbitrary concavity. These techniques are adaptive in the sense that every time
a candidate sample is rejected, the acceptance rate is improved. The two
proposed algorithms can work properly when the target pdf is multimodal, with
first and second derivatives analytically intractable, and when the tails are
log-convex in a infinite domain. Therefore, they can be applied in a number of
scenarios in which the other generalizations of the standard ARS fail. Two
illustrative numerical examples are shown.

Computation;Applications