Oksana Chkrebtii (Ohio State University) will give an online mini-course on spatial modeling and inference with Gaussian processes. The course is intended for students in mathematics, statistics, and related disciplines in their 3rd year and above or for beginning graduate students, as well as for anyone interested in related topics. Students should have taken calculus and linear algebra as well as be familiar with elementary probability theory (random variables, expectations, standard family distributions, etc.) and basic concepts of mathematical statistics (parameter estimation, uncertainty quantification, linear regression). Some programming experience will be helpful, as all mathematical concepts will be illustrated with computations. Lectures will be given in English.

A common problem in the natural sciences and engineering is to learn a smooth spatial field from data observed at discrete locations. Applications range from remote sensing and mineral exploration, to building model surrogates. Gaussian processes (GPs) are a flexible class of models used for describing spatial data and performing statistical inference on the unknown spatial field. This course begins with an introduction to the multivariate normal distribution and proceeds to define GPs with many examples presented along the way. Properties of GPs are discussed with a focus on understanding smoothness. The use of GPs for function estimation and uncertainty quantification is discussed and illustrated in practice.

Software requirements: RStudio and R (4.5.1 or above) are required. Students are encouraged to set up the computing environment in advance by following the instructions in the “Getting set up” section (https://www.bayesrulesbook.com/preface#setup) of the following textbook, freely available online: https://www.bayesrulesbook.com.

Oksana Chkrebtii is a Professor in the Department of Statistics and the Department of Materials Science and Engineering (by courtesy) at the Ohio State University. She completed her undergraduate and Master’s degrees in Statistics at Carleton University in Ottawa (Canada) and received her PhD in Statistics from Simon Fraser University (Canada). Prof. Chkrebtii research focuses on statistical inference for dynamical systems models, including those defined by ordinary and partial differential equations, stochastic differential equations, and other stochastic generative models.