Peter Green's 1995 contribution to Bayesian statistics
Reversible-jump Markov chain Monte Carlo (RJMCMC), introduced by statistician Peter Green in 1995, lets a Bayesian sampler jump between models that have different numbers of parameters — making it a cornerstone method for model selection.
Most Markov chain Monte Carlo methods explore a single, fixed-size model. Peter Green's reversible-jump MCMC — set out in a 1995 paper in Biometrika — removed that limit, letting the sampler move between models of different dimension (say, deciding how many components a mixture should have) while keeping the mathematics valid.
That “trans-dimensional” move turned out to be enormously useful, and RJMCMC is now a standard tool across statistics, genetics and signal processing. Green, a Fellow of the Royal Society, is emeritus professor at the University of Bristol.
Sources: Peter Green (statistician), Wikipedia · Biometrika (1995)