Among Barndorff-Nielsen's early scientific contributions are his work on exponential families and on the foundations of statistics, in particular sufficiency and conditional inference. In 1977 he introduced the hyperbolic distribution as a mathematical model of the size distribution of sand grains, formalising heuristic ideas proposed by Ralph Alger Bagnold. He also derived the larger class of generalised hyperbolic distributions. These distributions, in particular the normal-inverse Gaussian distribution, have later turned out to be useful in many other areas of science, in particular turbulence and finance. The NIG-distribution is now widely used to describe the distribution of returns from financial assets. In 1984 he produced a short film on the physics of blown sand and the life of the British scientist and explorer Brigadier Ralph Alger Bagnold. A follow up to the film was produced in 2011 on the studies of stochastics in the physical sciences carried out by Barndorff-Nielsen and colleagues at the Faculty of Science, Aarhus University by the initiative of the President of the Bernoulli Society for Mathematical Statistics and Probability, Professor Victor Pérez-Abreu. Later Barndorff-Nielsen played a leading role in the application of differential geometry to investigate statistical models. Another main contribution is his work on asymptotic methods in statistics, not least his formula for the conditional distribution of the maximum likelihood estimator given an ancillary statistic that generalizes a formula by Ronald A. Fisher. He has jointly with David Cox written two influential books on asymptotic techniques in statistics. Since the mid-90s Barndorff-Nielsen has worked on stochastic models in finance and turbulence, on statistical methods for the analysis of data from experiments in quantum physics, and has contributed to the theory ofLévy processes.
Notable honors and positions held
Barndorff-Nielsen is a member of the Royal Danish Academy of Sciences and Letters and of Academia Europaea. He has received honorary doctorate degrees from the Université Paul Sabatier, Toulouse and the Katholieke Universiteit Leuven. In 1993-1995 he was a very influential president of the Bernoulli Society for Mathematical Statistics and Probability. He was the editor of International Statistical Review in 1980-1987 and of the journal Bernoulli in 1994–2000. From 1 April 1998 to 31 March 2003 he was Scientific Director of MaPhySto, which was a centre devoted to advanced research and training in the fields of mathematical physics and stochastics, as well as some closely related areas. In 2001 he received the Humboldt Prize and in 2010 the Faculty Price from Faculty of Science, Aarhus University.