Grad Student Seminar: Samopriya Basu, Jack Prothero
Fiducial inference for SDEs with constant diffusion
In this talk, I will talk about my research with my advisor Prof. Jan Hannig on carrying out fiducial inference for stochastic ordinary differential equations with constant diffusion coëfficient. The diffusion coëfficient σ is unknown and the drift term can depend on any number of unknown parameters β, and the task is to come up with a data-dependent distribution estimator Fid(·) on the parameter space Θ ⊂ ℝ+ × ℝp+1, called the fiducial distribution, for the parameter vector θT = (σ, βT) by “inverting” the law Pθ of the observable quantity of interest Q(θ), and to efficiently sample from it. I will discuss the challenges associated with carrying out fiducial inference in such settings and some of our resolutions thereof inspired by some approximation techniques in the Uncertainty Quantification literature.
Centering in Functional Data Analysis
Data matrix centering is an ever-present yet underexamined aspect of data analysis. Centering such that data features have mean zero is often the default operation, but in many contexts the standard centering practice is less clear and the broader consequences of centering are less understood. We present the effects of different forms of centering formally alongside a unified terminology for such operations. We then explore data where different forms of centering enhance interpretability of analytic results. Finally, we present a novel statistical test to determine whether additional centering may be appropriate for a given data matrix.