Statistics and Computing

, Volume 21, Issue 4, pp 633–647 | Cite as

A generalization of the adaptive rejection sampling algorithm

  • Luca Martino
  • Joaquín Míguez


Rejection sampling is a well-known method to generate random samples from arbitrary target probability distributions. It demands the design of a suitable proposal probability density function (pdf) from which candidate samples can be drawn. These samples are either accepted or rejected depending on a test involving the ratio of the target and proposal densities. The adaptive rejection sampling method is an efficient algorithm to sample from a log-concave target density, that attains high acceptance rates by improving the proposal density whenever a sample is rejected. In this paper we introduce a generalized adaptive rejection sampling procedure that can be applied with a broad class of target probability distributions, possibly non-log-concave and exhibiting multiple modes. The proposed technique yields a sequence of proposal densities that converge toward the target pdf, thus achieving very high acceptance rates. We provide a simple numerical example to illustrate the basic use of the proposed technique, together with a more elaborate positioning application using real data.


Rejection sampling Adaptive rejection sampling Gibbs sampling Monte Carlo integration Sensor networks Target localization 


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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Department of Signal Theory and CommunicationsUniversidad Carlos III de MadridLeganésSpain

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