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Adaptive Rejection Metropolis Sampling Within Gibbs Sampling
Author(s) -
Gilks W. R.,
Best N. G.,
Tan K. K. C.
Publication year - 1995
Publication title -
journal of the royal statistical society: series c (applied statistics)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.205
H-Index - 72
eISSN - 1467-9876
pISSN - 0035-9254
DOI - 10.2307/2986138
Subject(s) - gibbs sampling , metropolis–hastings algorithm , sampling (signal processing) , rejection sampling , slice sampling , statistics , sampling design , importance sampling , adaptive sampling , mathematics , econometrics , computer science , monte carlo method , markov chain monte carlo , sociology , bayesian probability , hybrid monte carlo , demography , population , filter (signal processing) , computer vision
SUMMARY Gibbs sampling is a powerful technique for statistical inference. It involves little more than sampling from full conditional distributions, which can be both complex and computationally expensive to evaluate. Gilks and Wild have shown that in practice full conditionals are often log‐concave, and they proposed a method of adaptive rejection sampling for efficiently sampling from univariate log‐concave distributions. In this paper, to deal with non‐log‐concave full conditional distributions, we generalize adaptive rejection sampling to include a Hastings‐Metropolis algorithm step. One important field of application in which statistical models may lead to non‐log‐concave full conditionals is population pharmacokinetics. Here, the relationship between drug dose and blood or plasma concentration in a group of patients typically is modelled by using nonlinear mixed effects models. Often, the data used for analysis are routinely collected hospital measurements, which tend to be noisy and irregular. Consequently, a robust ( t ‐distributed) error structure is appropriate to account for outlying observations and/or patients. We propose a robust nonlinear full probability model for population pharmacokinetic data. We demonstrate that our method enables Bayesian inference for this model, through an analysis of antibiotic administration in new‐born babies.