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, but now known as the Barndorff-Nielsen formula).
Barndorff-Nielsen's work on differential geometry and asymptotic methods in statistics is notable for its application to statistical modeling. His formula for the conditional distribution of the maximum likelihood estimator given an ancillary statistic generalizes a formula by Ronald A. Fisher (originally called the -formula, but now known as the Barndorff-Nielsen formula).