A Modified Adaptive Accept-Reject Algorithm for Univariate Densities with Bounded Support

The need to simulate from a univariate density arises in several settings, particularly in Bayesian analysis. An especially efficient algorithm which can be used to sample from a univariate density, fX , is the adaptive accept-reject algorithm. To implement the adaptive accept-reject algorithm, the user has to envelope T ◦ fX , where T is some transformation such that the density g(x) ∝ T−1 (α + βx) is easy to sample from. Successfully enveloping T ◦ fX , however, requires that the user identify the number and location of T ◦ fX ’s inflection points. This is not always a trivial task. In this paper we propose an adaptive accept-reject algorithm which relieves the user of precisely identifying the location of T ◦ fX ’s inflection points. This new algorithm is shown to be efficient and can be used to sample from any density such that its support is bounded and its log is three-times differentiable.