APPM Colloquium - Peter F. Craigmile
Peter F. Craigmile, Department of Statistics, The Ohio State ³Ô¹ÏÍø
Enhancing statistical inference for stochastic processes using modern statistical methods
(This is joint research with Radu Herbei, Matthew Pratola, Huong Nguyen, and Grant Schneider, at The Ohio State ³Ô¹ÏÍø.)
Stochastic processes such as stochastic differential equations (SDEs) and Gaussian processes are used as statistical models in many disciplines. ÌýHowever there are many situations in which a statistical design or inference problem associated with these processes is intractable, and approximations are then required. ÌýTraditionally these approximations often come without measures of quality.
We motivate using three examples:
(i) Approximating intractable likelihoods for SDEs;
(ii) Using "near-optimal design" to find spatial designs that minimize
integrated mean square error;
(iii) Using well-designed data subsets to enhance stochastic gradient
descent (SGD) for big data statistical learning.
We demonstrate approaches to framing such problems from a statistical perspective so that we can probabilistically quantify uncertainties when making approximations. ÌýDepending on the problem, we achieve this using a range of modern statistical methods such as Gaussian processes, point processes, sampling theory, sequential design, and quantile regression.