Read before the Royal Statistical Society at the 1992 meeting on "The Gibbs sampler and other Markov chain Monte Carlo methods" — the gathering that launched MCMC into mainstream statistics — this paper (from the MRC Biostatistics Unit, Cambridge) surveys the breadth of medical applications of Gibbs sampling. It shows one estimation engine handling longitudinal, spatial, covariate-measurement-error, and survival models across immunology, pharmacology, transplantation, cancer screening, industrial epidemiology, and genetic epidemiology. The unifying message: complex medical models that used to demand bespoke, problem-specific methodology can instead be fit by a single generic device.
"Gibbs sampling succeeds because it reduces the problem of dealing simultaneously with a large number of intricately related unknown parameters and missing data into a much simpler problem of dealing with one unknown quantity at a time, sampling each from its full conditional distribution."
This is a period document from the exact moment Bayesian computation stopped being a theoretical curiosity and became a practical toolkit — the RSS 1992 meeting is the hinge, and this is the paper that argued the case from applications rather than theory. Its lasting significance is less any single model than the demonstration that one algorithm could dissolve the boilerplate of problem-specific estimation across all of biostatistics, which is precisely the abstraction that BUGS/WinBUGS then packaged for non-specialists. On the wiki it ties the Gibbs sampler to its applied lineage and connects the frailty (Clayton 1991) and disease-mapping threads to their shared computational root. The candid caveat is the authors' own: at the time the evidence base was mostly their own group's work, so it reads as much as a manifesto as a survey.