A selective view of stochastic inference and modeling problems in nanoscale biophysics

Advances in nanotechnology enable scientists for the first time to study biological processes on a nanoscale molecule-by-molecule basis. They also raise challenges and opportunities for statisticians and applied probabilists. To exemplify the stochastic inference and modeling problems in the field, this paper discusses a few selected cases, ranging from likelihood inference, Bayesian data augmentation, and semi- and non-parametric inference of nanometric biochemical systems to the utilization of stochastic integro-differential equations and stochastic networks to model single-molecule biophysical processes. We discuss the statistical and probabilistic issues as well as the biophysical motivation and physical meaning behind the problems, emphasizing the analysis and modeling of real experimental data. This work was supported by the United States National Science Fundation Career Award (Grant No. DMS-0449204)