A generalization of the adaptive rejection sampling algorithm
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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.
KeywordsRejection sampling Adaptive rejection sampling Gibbs sampling Monte Carlo integration Sensor networks Target localization
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- Ali, A.M., Yao, K., Collier, T.C., Taylor, E., Blumstein, D., Girod, L.: An empirical study of collaborative acoustic source localization. In: Proceedings Information Processing in Sensor Networks, IPSN07, Boston (2007) Google Scholar
- Gilks, W.R.: Derivative-free adaptive rejection sampling for Gibbs sampling. Bayesian Stat. 4, 641–649 (1992) Google Scholar
- Gilks, W.R., Robert, N.G.O., George, E.I.: Adaptive direction sampling. J. R. Stat. Soc., Ser. D Stat. 43(1), 179–189 (1994) Google Scholar
- Görür, D., Teh, Y.W.: Concave convex adaptive rejection sampling. Technical Report, University College, London (2009) Google Scholar
- Kotecha, J.H., Djurić, P.M.: Gibbs sampling approach for generation of truncated multivariate Gaussian random variables. In: Proceedings of the IEEE ICASSP, vol. 3, pp. 1757–1760 (1999) Google Scholar
- Mayo, P., Rodenas, F., Verdú, G.: Comparing methods to denoise mammographic images. In: Proceedings of the 26th IEEE EMBS, vol. 1, pp. 247–250 (2004) Google Scholar
- Rappaport, T.S.: Wireless Communications: Principles and Practice, 2nd edn. Prentice-Hall, Upper Saddle River (2001) Google Scholar