Professor Peter Green

Scheel, I., Green, P.J. & Rougier, J.C. 2011, 'A graphical diagnostic for identifying influential model choices in bayesian hierarchical models', Scandinavian Journal of Statistics, vol. 38, no. 3, pp. 1-22.
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Real-world phenomena are frequently modelled by Bayesian hierarchical models. The building-blocks in such models are the distribution of each variable conditional on parent and/or neighbour variables in the graph. The specifications of centre and spread of these conditional distributions may be well motivated, whereas the tail specifications are often left to convenience. However, the posterior distribution of a parameter may depend strongly on such arbitrary tail specifications. This is not easily detected in complex models. In this article, we propose a graphical diagnostic, the Local critique plot, which detects such influential statistical modelling choices at the node level. It identifies the properties of the information coming from the parents and neighbours (the local prior) and from the children and co-parents (the lifted likelihood) that are influential on the posterior distribution, and examines local conflict between these distinct information sources. The Local critique plot can be derived for all parameters in a chain graph model.

Green, P.J. & Mortera, J. 2009, 'Sensitivity of inferences in forensic genetics to assumptions about founding genes', Annals of Applied Statistics, vol. 3, no. 2, pp. 731-763.
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Many forensic genetics problems can be handled using structured systems of discrete variables, for which Bayesian networks offer an appealing practical modeling framework, and allow inferences to be computed by probability propagation methods. However, w

Ruffieux, Y. & Green, P.J. 2009, 'Alignment of multiple configurations using hierarchical models', Journal Of Computational And Graphical Statistics, vol. 18, no. 3, pp. 756-773.
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We describe a method for aligning multiple unlabeled configurations simultaneously, Specifically. we extend the two-con figuration matching approach of Green and Mardia (2006) to the multiple configuration setting. Our approach is based on the introducti

Thomas, A. & Green, P.J. 2009, 'Enumerating the decomposable neighbors of a decomposable graph under a simple perturbation scheme', Computational Statistics & Data Analysis, vol. 53, no. 4, pp. 1232-1238.
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Given a decomposable graph, we characterize and enumerate the set of pairs of vertices whose connection or disconnection results in a new graph that is also decomposable. We discuss the relevance of these results to Markov chain Monte Carlo methods that

Thomas, A. & Green, P.J. 2009, 'Enumerating The Junction Trees Of A Decomposable Graph', Journal of Computational and Graphical Statistics, vol. 18, no. 4, pp. 930-940.
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We derive methods for enumerating the distinct junction tree representations for any given decomposable graph. We discuss the relevance of the method to estimating conditional independence graphs of graphical models and give an algorithm that, given a ju

Hosking, F.J., Sterne, J.A., Smith, G.D. & Green, P.J. 2008, 'Inference from genome-wide association studies using a novel Markov model', Genetic Epidemiology, vol. 32, no. 6, pp. 497-504.
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In this paper we propose a Bayesian modeling approach to the analysis of genome-wide association studies based on single nucleotide polymorphism (SNP) data. Our latent seed model combines various aspects of k-means clustering, hidden Markov models (HMMs)

Hurn, M., Green, P.J. & Al-awadhi, F. 2008, 'A Bayesian hierarchical model for photometric red shifts', Journal of the Royal Statistical Society Series C: Applied Statistics, vol. 57, no. 4, pp. 487-504.
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The Sloan digital sky survey is an extremely large astronomical survey that is conducted with the intention of mapping more than a quarter of the sky. Among the data that it is generating are spectroscopic and photometric measurements, both containing in

Mardia, K.V., Nyirongo, V.B., Green, P.J., Gold, N.D. & Westhead, D.R. 2007, 'Bayesian refinement of protein functional site matching', BMC Bioinformatics, vol. 8, no. 1, pp. 1-18.
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Background: Matching functional sites is a key problem for the understanding of protein function and evolution. The commonly used graph theoretic approach, and other related approaches, require adjustment of a matching distance threshold a priori accordi

Green, P.J. & Mardia, K.V. 2006, 'Bayesian alignment using Hierarchical models, with applications in protein bioinformatics', Biometrika, vol. 93, no. 2, pp. 235-254.
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An important problem in shape analysis is to match configurations of points in space after filtering out some geometrical transformation. In this paper we introduce hierarchical models for such tasks, in which the points in the configurations are either

Lau, J. & Green, P.J. 2006, 'Bayesian model-based clustering procedures', Journal of Computational and Graphical Statistics, vol. 16, no. 3, pp. 526-558.
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This paper establishes a general framework for Bayesian model-based clustering, in which subset labels are exchangeable, and items are also exchangeable, possibly up to covariate e«ects. It is rich enough to encompass a variety of existing procedures, including some recently discussed methodologies involving stochastic search or hierarchical clustering, but more importantly allows the formulation of clustering procedures that are optimal with respect to a speci»ed loss function. Our focus is on loss functions based on pairwise coincidences, that is, whether pairs of items are clustered into the same subset or not.

Hein, A.K., Richardson, S., Causton, H.C., Ambler, G.K. & Green, P.J. 2005, 'BGX: A fully Bayesian integrated approach to the analysis of affymetrix genechip data', Biostatistics, vol. 6, no. 3, pp. 349-373.
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We present Bayesian hierarchical models for the analysis of Affymetrix GeneChip data. The approach we take differs from other available approaches in two fundamental aspects. Firstly, we aim to integrate all processing steps of the raw data in a common s

Nott, D. & Green, P.J. 2004, 'Bayesian variable selection and the Swendsen-Wang slgorithm', Journal Of Computational And Graphical Statistics, vol. 13, no. 1, pp. 141-157.
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The need to explore model uncertainty in linear regression models with many predictors has motivated improvements in Markov chain Monte Carlo sampling algorithms for Bayesian variable selection. Currently used sampling algorithms for Bayesian variable se

Green, P.J. 2003, 'Diversities of gifts, but the same spirit', Journal Of The Royal Statistical Society Series D-The Statistician, vol. 52, pp. 423-435.
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This address reviews the great diversity of the discipline of statistics, seeking an essential unity among its various aspects. The role of statistical modelling in underpinning the subject is stressed. To safeguard the discipline in the future, it is se

Scaccia, L. & Green, P.J. 2003, 'Bayesian growth curves using normal mixtures with nonparametric weights', Journal Of Computational And Graphical Statistics, vol. 12, no. 2, pp. 308-331.
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Reference growth curves estimate the distribution of a measurement as it changes according to some covariate, often age. We present a new methodology to estimate growth curves based on mixture models and splines. We model the distribution of the measurem

Fernandez, C. & Green, P.J. 2002, 'Modelling spatially correlated data via mixtures: A Bayesian approach', Journal Of The Royal Statistical Society Series B-Statistical Methodology, vol. 64, no. 1, pp. 805-826.
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The paper develops mixture models for spatially indexed data. We confine attention to the case of finite, typically irregular, patterns of points or regions with prescribed spatial relationships, and to problems where it is only the weights in the mixtur

Green, P.J. & Richardson, S. 2002, 'Hidden Markov models and disease mapping', Journal Of The American Statistical Association, vol. 97, no. 460, pp. 1055-1070.
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We present new methodology to extend hidden Markov models to the spatial domain, and use this class of models to analyze spatial heterogeneity of count data on a rare phenomenon. This situation occurs commonly in many domains of application, particularly

Richardson, S., Leblond, L., Jaussent, I. & Green, P.J. 2002, 'Mixture models in measurement error problems, with reference to Epidemiological studies', Journal Of The Royal Statistical Society Series A-Statistics In Society, vol. 165, no. 1, pp. 549-566.
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The paper focuses on a Bayesian treatment of measurement error problems and on the question of the specification of the prior distribution of the unknown covariates. It presents a flexible semiparametric model for this distribution based on a mixture of

Viallefont, V., Richardson, S. & Green, P.J. 2002, 'Bayesian analysis Of Poisson mixtures', Journal Of Nonparametric Statistics, vol. 14, no. 1-Feb, pp. 181-202.
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The modelling of rare events via a Poisson distribution sometimes reveals substantial over-dispersion, indicating that some unexplained discontinuity arises in the data. We suggest modelling this over-dispersion by a Poisson mixture. In a hierarchical Ba

Green, P.J. & Richardson, S. 2001, 'Modelling heterogeneity with and without the dirichlet process', Scandinavian Journal Of Statistics, vol. 28, no. 2, pp. 355-375.
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We investigate the relationships between Dirichlet process (DP) based models and allocation models for a variable number of components, based on exchangeable distributions. It is shown that the DP partition distribution is a Limiting case of a Dirichlet-

Cook, R., Pardoe, L., Gelfand, A., Green, P.J., Hastie, T. & Tibshirani, R. 2000, 'Bayesian backfitting - Comments and rejoinder', Statistical Science, vol. 15, no. 3, pp. 213-223.
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Davino, F., Frigessi, A. & Green, P.J. 2000, 'Penalized pseudolikelihood inference in spatial interaction models with covariates', Scandinavian Journal Of Statistics, vol. 27, no. 3, pp. 445-458.
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Given spatially located observed random variables ((x) under bar, (z) under bar) = {(x(i), z(i))}(i), we propose a new method for non-parametric estimation of the potential functions of a Markov random field p((x) under bar\(z) under bar), based on a rou

Nobile, A. & Green, P.J. 2000, 'Bayesian analysis of factorial experiments by mixture modelling', Biometrika, vol. 87, no. 1, pp. 15-35.
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A Bayesian analysis for factorial experiments is presented, using finite mixture distributions to model the main effects and interactions. This allows both estimation and an analogue of hypothesis testing in a posterior analysis using a single prior spec

Giudici, P. & Green, P.J. 1999, 'Decomposable graphical Gaussian model determination', Biometrika, vol. 86, no. 4, pp. 785-801.
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We propose a methodology for Bayesian model determination in decomposable graphical Gaussian models. To achieve this aim we consider a hyper inverse Wishart prior distribution on the concentration matrix for each given graph. To ensure compatibility acro

Ganesh, A., Green, P.J., Oconnell, N. & Pitts, S. 1998, 'Bayesian network management', Queueing Systems, vol. 28, no. 1-Mar, pp. 267-282.
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We formulate some general network (and risk) management problems in a Bayesian context, and point out some of the essential features. We argue and demonstrate that, when one is interested in rare events, the Bayesian and frequentist approaches can lead t

Murdoch, D. & Green, P.J. 1998, 'Exact sampling from a continuous state space', Scandinavian Journal Of Statistics, vol. 25, no. 3, pp. 483-502.
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Propp & Wilson (1996) described a protocol, called coupling from the past, for exact sampling from a target distribution using a coupled Markov chain Monte Carlo algorithm. In this paper,ve extend coupling from the past to various MCMC samplers on a cont

Pievatolo, A. & Green, P.J. 1998, 'Boundary detection through dynamic polygons', Journal Of The Royal Statistical Society Series B-Statistical Methodology, vol. 60, no. 1, pp. 609-626.
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A method for the Bayesian restoration of noisy binary images portraying an object with constant grey level on a background is presented. The restoration, performed by fitting a polygon with any number of sides to the objects outline, is driven by a new p

Richardson, S. & Green, P.J. 1997, 'On bayesian analysis of mixtures with an unknown number of components', Journal Of The Royal Statistical Society Series B-Methodological, vol. 59, no. 4, pp. 731-758.
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New methodology for fully Bayesian mixture analysis is developed, making use of reversible jump Markov chain Monte Carlo methods that are capable of jumping between the parameter subspaces corresponding to different numbers of components in the mixture.

Besag, J., Green, P.J., Higdon, D. & Mengersen, K. 1995, 'Bayesian computation and stochastic-systems', Statistical Science, vol. 10, no. 1, pp. 3-41.
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Markov chain Monte Carlo (MCMC) methods have been used extensively in statistical physics over the last 40 years, in spatial statistics for the past 20 and in Bayesian image analysis over the last decade. In the last five years, MCMC has been introduced

Green, P.J. 1995, 'Reversible jump Markov chain Monte Carlo computation and Bayesian model determination', Biometrika, vol. 82, no. 4, pp. 711-732.
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Markov chain Monte Carlo methods for Bayesian computation have until recently been restricted to problems where the joint distribution of all variables has a density with respect to some fixed standard underlying measure. They have therefore not been ava

Besag, J. & Green, P.J. 1993, 'Spatial statistics and bayesian computation', Journal Of The Royal Statistical Society Series B-Methodological, vol. 55, no. 1, pp. 25-37.
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Markov chain Monte Carlo (MCMC) algorithms, such as the Gibbs sampler, have provided a Bayesian inference machine in image analysis and in other areas of spatial statistics for several years, founded on the pioneering ideas of Ulf Grenander. More recentl

Cole, T. & Green, P.J. 1992, 'Smoothing reference centile curves - The LMS method and penalized likelihood', Statistics In Medicine, vol. 11, no. 10, pp. 1305-1319.
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Reference centile curves show the distribution of a measurement as it changes according to some covariate, often age. The LMS method summarizes the changing distribution by three curves representing the median, coefficient of variation and skewness, the

Aykroyd, R. & Green, P.J. 1991, 'Global and local priors, and the location of lesions using gamma-camera imagery', Philosophical Transactions Of The Royal Society Of London Series A-Mathematical Physical And Engineering Sciences, vol. 337, no. 1647, pp. 323-342.
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After a brief review of the paradigm of bayesian image restoration, we pose the question: If high-level prior information is available and usable, what is lost by modelling at the pixel level instead? Our discussion is based on a real application where t

Green, P.J. 1991, 'Bayesian image-restoration, with 2 applications in spatial statistics - Discussion', Annals Of The Institute Of Statistical Mathematics, vol. 43, no. 1, pp. 22-24.
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Green, P.J. 1990, 'Bayesian reconstructions from emission tomography data using a modified EM algorithm', IEEE Transactions On Medical Imaging, vol. 9, no. 1, pp. 84-93.
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Green, P.J. 1990, 'On use of the EM algorithm for penalized likelihood estimation', Journal of The Royal Statistical Society Series B-methodological, vol. 52, no. 3, pp. 443-452.
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The EM algorithmis a popular approach to maximuml ikelihoode stimationb ut has not been muchu sed forp enalizedl ikelihoodo r maximuma posteriori estimation.T his paper discussesp ropertieos f theE M algorithmin suchc ontextsc, oncentratinogn rateso f convergence, and presentsa n alternativet hati s usuallym ore practicala nd convergesa t least as quickly

Green, P.J. 1988, 'Regression, curvature and weighted least-squares', Mathematical Programming, vol. 42, no. 1, pp. 41-51.
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Green, P.J. 1987, 'Penalized likelihood for general semiparametric regression-models', International Statistical Review, vol. 55, no. 3, pp. 245-259.
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Lenth, R.V. & Green, P.J. 1987, 'Consistency of deviance-based M estimators', Journal of The Royal Statistical Society Series B-methodological, vol. 49, no. 3, pp. 326-330.
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In a general estimation problem, the deviance function generates statistics that are similar to squared standardized residuals. A deviance-based M estimator (DBME) is defined as an adaptively weighted maximum-likelihood estimator, where the weights depend upon the deviances. In both a single-parameter and a regression setting, we give some general conditions under which a DMBE is consistent. For a suitable weighting scheme, these conditions are satisfied in many continuous Cramer-Rao-regular families and in related linear or nonlinear regression cases. The conditions fail (and the estimator is inconsistent) in most discrete families.

Green, P.J., Jennison, C. & Seheult, A. 1985, 'Analysis of field experiments by least-squares smoothing', Journal of The Royal Statistical Society Series B-methodological, vol. 47, no. 2, pp. 299-315.
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Assuminga smooth trendp lus independente rrorm odel fort he environmentael ffects in the yields of a fieldp lot experiment,le ast squares smoothingm ethodsa re developed to estimate both the treatmente ffectsa nd the unknown trend. Treatmente stimates are closely related to those resultingf roma generalizedl east squares analysisi n which the covariance structuref or the environmentael ffectsh as a particularf orm.H owever, the main emphases are on the accuracy of treatmente stimatesu nder a fixed smooth trend plus error model and the exploratory power of the basic method to isolate trende ffectso f unknownf orm. Althought he detailed developmenti s for the one-dimensionalc ase, generalizations of the smoothness concept and extensions to two dimensions are also discussed. Application of the basic method is illustrated on three data sets and the results compared with other analyses.

Green, P.J. 1985, 'Linear-models for field trials, smoothing and cross-validation', Biometrika, vol. 72, no. 3, pp. 527-537.
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Green, P.J. 1984, 'Iteratively reweighted least-squares for maximum-likelihood estimation, and some robust and resistant alternatives', Journal Of The Royal Statistical Society Series B-Methodological, vol. 46, no. 2, pp. 149-192.
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Wright, B., Green, P.J. & Braiden, P. 1982, 'Quantitative-analysis of delayed fracture observed in stress rate tests on brittle materials', Journal Of Materials Science, vol. 17, no. 11, pp. 3227-3234.
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Green, P.J. 1981, 'Modeling yeast-cell growth using stochastic branching-processes', Journal Of Applied Probability, vol. 18, no. 4, pp. 799-808.
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Nelson, S. & Green, P.J. 1981, 'The random transition model of the cell-cycle - A critical-review', Cancer Chemotherapy And Pharmacology, vol. 6, no. 1, pp. 11-18.
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Green, P.J. & Silverman, B. 1979, 'Constructing the convex hull of a set of points in the plane', Computer Journal, vol. 22, no. 3, pp. 262-266.
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Green, P.J. & Sibson, R. 1978, 'Computing dirichlet tessellations in plane', Computer Journal, vol. 21, no. 2, pp. 168-173.
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Green, P.J. 1977, 'Conditional limit-theorems for general branching-processes', Journal Of Applied Probability, vol. 14, no. 3, pp. 451-463.
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Green, P.J. 1977, 'Conditioning a branching-process on non-extinction', Mathematical Biosciences, vol. 35, no. 3-4, pp. 261-265.
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Barnett, V., Green, P.J. & Robinson, A. 1976, 'Concomitants and correlation estimates', Biometrika, vol. 63, no. 2, pp. 323-328.
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Green, P.J. 1976, 'The maximum and time to absorption of a left-continuous random walk', Journal Of Applied Probability, vol. 13, no. 3, pp. 444-454.
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For a left-continuous random walk, absorbing at 0, the joint distribution of the maximum and time to absorption is derived. A description of the tails of the distributions and a conditional limit theorem are obtained for the cases where absorption is certain.

Green, P.J. 1976, 'Maximum and time to absorption of a left-continuous random-walk', Journal Of Applied Probability, vol. 13, no. 3, pp. 444-454.
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Green, P.J., Noad, R., Smart, N. 2005, 'Further hidden Markov model cryptanalysis', Workshop on Cryptographic Hardware and Embedded Systems, Edinburgh, UK, August 2005 in Cryptographic Hardware And Embedded Systems - CHES 2005, Proceedings, ed Josyula R. Rao, Berk Sunar, Springer-Verlag Berlin, Berlin, pp. 61-74.
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We extend the model of Karlof and Wagner for modelling side channel attacks via Input Driven Hidden Markov Models (IDHMM) to the case where not every state corresponds to a single observable symbol. This allows us to examine algorithms where errors in me