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, f(X), is the adaptive accept-reject algorithm. To implement the adaptive accept-reject algorithm, the user has to envelope T circle f(X), where T is some transformation such that the density g(x) proportional to T(-1) (alpha + beta x) is easy to sample from. Successfully enveloping T circle f(X), however, requires that the user identify the number and location of T circle f(X)'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 circle f(X)'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.