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== Slice-within-Gibbs sampling ==
In a [[Gibbs sampling|Gibbs sampler]], one needs to draw efficiently from all the full-conditional distributions. When sampling from a full-conditional density is not easy, a single iteration of slice sampling or the Metropolis-Hastings algorithm can be used within-Gibbs to sample from the variable in question. If the full-conditional density is log-concave, a more efficient alternative is the application of [[Rejection sampling|adaptive rejection sampling]] (ARS) methods.<ref>{{Cite journal|title = Adaptive Rejection Sampling for Gibbs Sampling|jstor = 2347565|journal = Journal of the Royal Statistical Society. Series C (Applied Statistics)|date = 1992-01-01|pages = 337–348|volume = 41|issue = 2|doi = 10.2307/2347565|first = W. R.|last = Gilks|first2 = P.|last2 = Wild}}</ref><ref>{{Cite journal|title = A Rejection Technique for Sampling from T-concave Distributions|journal = ACM Trans. Math. Softw.|date = 1995-06-01|issn = 0098-3500|pages = 182–193|volume = 21|issue = 2|doi = 10.1145/203082.203089|first = Wolfgang|last = Hörmann|citeseerx = 10.1.1.56.6055}}</ref><ref>{{Cite journal|title = A generalization of the adaptive rejection sampling algorithm|journal = Statistics and Computing|date = 2010-08-25|issn = 0960-3174|pages = 633–647|volume = 21|issue = 4|doi = 10.1007/s11222-010-9197-9|first = Luca|last = Martino|first2 = Joaquín|last2 = Míguez|hdl = 10016/16624}}</ref> When the ARS techniques cannot be applied (since the full-conditional is non-log-concave), the '''adaptive rejection Metropolis sampling algorithms''' are often employed.<ref>{{Cite journal|title = Adaptive Rejection Metropolis Sampling within Gibbs Sampling|jstor = 2986138|journal = Journal of the Royal Statistical Society. Series C (Applied Statistics)|date = 1995-01-01|pages = 455–472|volume = 44|issue = 4|doi = 10.2307/2986138|first = W. R.|last = Gilks|first2 = N. G.|last2 = Best|author2-link= Nicky Best |first3 = K. K. C.|last3 = Tan}}</ref><ref>{{Cite journal|title = Adaptive rejection Metropolis sampling using Lagrange interpolation polynomials of degree 2|journal = Computational Statistics & Data Analysis|date = 2008-03-15|pages = 3408–3423|volume = 52|issue = 7|doi = 10.1016/j.csda.2008.01.005|first = Renate|last = Meyer|first2 = Bo|last2 = Cai|first3 = François|last3 = Perron}}</ref><ref>{{Cite journal|title = Independent Doubly Adaptive Rejection Metropolis Sampling Within Gibbs Sampling|journal = IEEE Transactions on Signal Processing|date = 2015-06-01|issn = 1053-587X|pages = 3123–3138|volume = 63|issue = 12|doi = 10.1109/TSP.2015.2420537|first = L.|last = Martino|first2 = J.|last2 = Read|first3 = D.|last3 = Luengo|arxiv = 1205.5494}}</ref>
==Multivariate Methods==
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