Research

EM Videos

• Segmenting EM vidoes with an anode in them
• Segmenting Core shell videos

Uncertainty in Complex Computer Models

• Complex computer models, e.g. APSIM, are subject to several sources of uncertainty, including but not limited to:
  • imperfect knowledge about input and internal parameter values
  • the model’s imperfect representation of the true process

• Understanding how uncertainty in parameter and input values is propagated through the simulator informs future studies. That is, a thorough sensitivity analysis will identify which parameters require further investigation to reduce the uncertainty in the final product.

• Traditional sensitivity analysis methods require a large number of simulator runs. If the simulator takes a long time to run then sensitivity analysis is impractical and sometimes impossible. The use of efficient emulators or other approximations to the simulator is an important tool that allows for a complete sensitivity analysis of even the most complex computer models.

• Currently I am working to develop an efficient way to conduct a sensitivity analysis of APSIM that incorporates spatial and temporal effects using emulators.

Statistics in SO(3)

• My dissertation covered several topics about statistical methods for the rotation group SO(3)
  • Chapter two considers various intrinsic and extrinsic estimators for the central orientation (or mean) based on a sample of rotationally symmetric random rotations. This chapter also can be found in Technometrics.
  • Non-parametric confidence regions for the central orientation are considered in chapter three. An extended and polished version of this chapter can be found in the Journal of Multivariate Analysis.
  • Several asymptotic properties of the extrinsic median on SO(3) are derived and it is compared to the extrinsic mean with respect to efficiency and robustness in chapter four.
  • Chapter five describes the R package rotations, which can also can be found in The R Journal.
• Currently I am working on several related topics
  • I am developing a test for outliers in SO(3)
  • Introducing the concept of influence functions in SO(3)
  • Deriving asymptotic properties of intrinsic (geometeric) estimators for the central orientation