Anthony Davison has published on a wide range of topics in statistical theory and methods, and on environmental, biological and financial applications. His current main research interests are statistics of extremes, likelihood asymptotics, bootstrap and other resampling methods, and statistical modelling.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 15 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.He receive Guy Medal in Silver (2015) of the Royal Statistical Society.