Peter’s passing in September 2025 is a great loss to his friends and colleagues. He was a respected and widely admired statistician whose work drew on ideas from chemistry, physics and computer science. His bibliography reveals the broad range and impact of his contributions in these and other scientific disciplines. The Voter model, which Peter constructed with Aidan Sudbury when they were both working at the University of Bristol in the early seventies, was set out as a spatial model for competing species but became a focus for later theoretical work by mathematicians and physicists interested in non-equilibrium dynamics and critical phenomena. The model has seen application in areas ranging from ecology and political science to network theory and condensed matter physics. The Hammersley-Clifford Theorem, published in 1971 and derived by Peter and John Hammersley while the two were at Berkeley in the late sixties, has been of foundational importance for modern developments in spatial and graphical models and for Markov Chain Monte Carlo methods.

Peter considered model realism an important part of statistical modelling, and this led to physics-based models inspired by system dynamics, to Bayesian inference and Monte Carlo methods. In a 1993 discussion paper for the Royal Statistical Society Peter writes “Metropolis methods have been around for 40 years, and it has taken a very long time for the idea to percolate into the Bayesian community, where it naturally belongs … from now on we can compare our data with the model that we actually want to use rather than with a model which has some mathematically convenient form. This is surely a revolution”. Among many contributions to Monte Carlo theory and methods, his 1999 paper on Particle Filters, written at Oxford with James Carpenter and Paul Fearnhead, is an outstanding example, still widely cited in a fast-moving field.

After completing a BSc in Statistics at University College London in 1965, Peter went on to PhD studies at the University of California, Berkeley where he was supervised by Jerzy Neyman. On graduating in 1969 Peter moved to Tel Aviv (1969-70) and then on to Bristol (1970-75) where he was a lecturer. In 1976 he was appointed to a University Lectureship in the Mathematical Institute here in Oxford where he remained until 1989 when he joined the then newly established Department of Statistics as a Reader in Mathematical Statistics. Throughout this time, he was a Fellow and Tutor in Mathematics at Jesus College. He retired in 2010.

Peter is remembered in the department as an outstanding researcher in mathematical statistics and a thoughtful and generous colleague.

Prof Geoff Nicholls
Dept. of Statistics and St Peter’s College
University of Oxford