The goal of my academic work is to further the development of statistical science through teaching at all university levels, through the development and application of new approaches to data analysis, and through collaboration both within and outwith the EPFL.

Anthony Davison has published on a wide range of topics in statistical theory and methods, and on environmental, biological and financial applications. His main research interests are statistics of extremes, likelihood asymptotics, bootstrap and other resampling methods, and statistical modelling, with a particular focus on the first currently.
 
Statistics of extremes concerns rare events such as storms, high winds and tides, extreme pollution episodes, sporting records, and the like. The subject has a long history, but under the impact of engineering and environmental problems has been an area of intense development in the past 20 years. Davison''s PhD work was in this area, in a project joint between the Departments of Mathematics and Mechanical Engineering at Imperial College, with the aim of modelling potential high exposures to radioactivity due to releases from nuclear installations. The key tools developed, joint with Richard Smith, were regression models for exceedances over high thresholds, which generalized earlier work by hydrologists, and formed the basis of some important later developments. This has led to an ongoing interest in extremes, and in particular their application to environmental and financial data. A major current interest is the development of suitable methods for modelling rare spatio-temporal events, particularly but not only in the context of climate change.
 
 Likelihood asymptotics too have undergone very substantial development since 1980. Key tools here have been saddlepoint and related approximations, which can give remarkably accurate approximate distribution and density functions even for very small sample sizes. These approximations can be used for wide classes of parametric models, but also for certain bootstrap and resampling problems. The literature on these methods can seem arcane, but they are potentially widely applicable, and Davison wrote a book joint with Nancy Reid and Alessandra Brazzale intended to promote their use in applications.

Bootstrap methods are now used in many areas of application, where they can provide a researcher with accurate inferences tailor-made to the data available, rather than relying on large-sample or other approximations of doubtful validity. The key idea is to replace analytical calculations of biases, variances, confidence and prediction intervals, and other measures of uncertainty with computer simulation from a suitable statistical model. In a nonparametric situation this model consists of the data themselves, and the simulation simply involves resampling from the existing data, while in a parametric case it involves simulation from a suitable parametric model. There is a wide range of possibilities between these extremes, and the book by Davison and Hinkley explores these for many data examples, with the aim of showing how and when resampling methods succeed and why they can fail.

He was Editor of Biometrika (2008-2017), Joint Editor of Journal of the Royal Statistical Society, series B (2000-2003), editor of the IMS Lecture Notes – Monograph Series (2007), Associate Editor of Biometrika (1987-1999), and Associate Editor of the Brazilian Journal of Probability and Statistics (1987 – 2006). Currently he on the editorial board of Annual Reviews of Statistics and its Applications.  He has served on committees of Royal Statistical Society and of the Institute of Mathematical Statistics. He is an elected Fellow of the American Statistical Assocation and of the Institute of Mathematical Statistics, an elected member of the International Statistical Institute, and a Chartered Statistician.

In 2009 he was awarded a laurea honoris causa in Statistical Science by the University of Padova, in 2011 he held a Francqui Chair at Hasselt University, and in 2012 he was Mitchell Lecturer at the University of Glasgow. In 2015 he received the Guy Medal in Silver of the Royal Statistical Society and in 2018 was a Medallion Lecturer of the Institute of Mathematical Statistics.