A generalization of the adaptive rejection sampling algorithm

作者：Martino Luca^*; Miguez Joaquin

来源：Statistics and Computing, 2011, 21(4): 633-647.

DOI：10.1007/s11222-010-9197-9

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

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 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.

• 出版日期2011-10