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 (originally called the formula_1-formula, but now known as the Barndorff-Nielsen formula). 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 (often with Neil Shephard) and turbulence, on statistical methods for the analysis of data from experiments in quantum physics, and has contributed to the theory of Lévy processes.