Overview
Peter J. Green is a British statistician at the University of Bristol (Department of Mathematics), known primarily for introducing reversible jump Markov chain Monte Carlo (RJMCMC) in his landmark 1995 Biometrika paper. His framework extends the Metropolis-Hastings algorithm to trans-dimensional parameter spaces, enabling simultaneous Bayesian inference on model structure and parameters within a single Markov chain. Green has also made foundational contributions to spatial statistics, Bayesian computation, image analysis, and mixture modeling, including the authoritative Richardson-Green (1997) treatment of mixtures with an unknown number of components.
Key Contributions / Features
- RJMCMC (1995): Framework for reversible Markov chain samplers on spaces of varying dimension; dimension-matching bijection; Jacobian correction in acceptance ratio; hybrid sampler combining multiple move types; applications to change-point analysis, image segmentation, and partition models.
- Green-Sibson (1978): Algorithm for computing Dirichlet (Voronoi) tessellations in the plane — later used in the 2D image segmentation application of RJMCMC (§5 of Green 1995).
- Richardson-Green (1997): Bayesian analysis of Gaussian mixtures with unknown number of components via RJMCMC; the canonical application of RJMCMC to mixture modeling.
- Besag-Green-Higdon-Mengersen (1995): Major invited paper on Bayesian computation and stochastic systems (Statistical Science 10: 3–66).
- Green (1994): Discussion of Grenander-Miller jump-diffusion paper (J. R. Statist. Soc. B 56: 589–90), which anticipated the RJMCMC framework.
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