Peter J. Green (born 1950) is a British statistician at the University of Bristol whose invention of reversible jump Markov chain Monte Carlo (RJMCMC) in 1995 solved one of the most challenging problems in Bayesian computation: how to perform inference when the number of parameters itself is unknown. His method made it possible for a single MCMC chain to explore models of different dimensionalities, comparing and averaging across them in a principled Bayesian manner. This breakthrough has been applied to problems ranging from mixture model selection to phylogenetic tree reconstruction to image segmentation.
Education and Career
Green studied mathematics at the University of Oxford and received his PhD from the University of Sheffield. He joined the University of Bristol, where he has spent most of his career, becoming one of the leading figures in computational statistics and Bayesian methodology. He has also held visiting positions at numerous institutions worldwide.
Reversible Jump MCMC
The fundamental problem that reversible jump MCMC addresses is that standard MCMC methods operate within a parameter space of fixed dimension. But many statistical problems involve model uncertainty: how many components are in a mixture model? How many change points in a time series? How many clusters in the data? Green's RJMCMC extends the Metropolis-Hastings algorithm to allow moves between parameter spaces of different dimensions, maintaining the correct stationary distribution by constructing carefully designed proposals that match dimensions through auxiliary variables.
Before RJMCMC, Bayesian model comparison required computing marginal likelihoods separately for each model under consideration—a computationally expensive process that scaled poorly with the number of candidate models. Reversible jump MCMC instead explores the combined space of all models and their parameters simultaneously, automatically spending more time in regions of higher posterior probability and providing model probabilities as a natural byproduct of the sampling.
“The key idea of reversible jump is that we can unify model selection and parameter estimation into a single simulation framework, exploring a transdimensional parameter space.”— Peter Green
Applications
RJMCMC has been applied to a remarkable range of problems. In mixture modeling, it determines the number of components. In change-point analysis, it identifies the number and locations of change points. In genetics, it has been used for QTL mapping with an unknown number of loci. In ecology, it facilitates species distribution modeling. In image analysis, it performs object recognition with an unknown number of objects. The flexibility of the framework has made it one of the most widely used tools in modern Bayesian computation.
Other Contributions
Green has made important contributions to many other areas of statistics, including penalized likelihood methods (particularly penalized splines), graphical models, Bayesian nonparametrics, and computational geometry applied to statistics. His work on decomposable graphical models and Bayesian model determination for graphical models has been particularly influential.
Recognition
Green has received the Guy Medal in Silver and in Bronze from the Royal Statistical Society, has been elected a Fellow of the Royal Society, and has received numerous other honors. The reversible jump MCMC paper is one of the most cited papers in the history of statistics, and the method it introduced has become a standard part of the Bayesian computational toolkit.
Born in England.
Received PhD from the University of Sheffield.
Joined the University of Bristol.
Published “Reversible jump Markov chain Monte Carlo computation and Bayesian model determination” in Biometrika.
Elected Fellow of the Royal Society.
Received the Guy Medal in Silver from the Royal Statistical Society.