Subhadra Dasgupta, IITB-Monash Research Academy

• Title: G-optimal retrospective grid designs

• Abstract: This work is focused on finding the best possible retrospective designs for kriging models with two-dimensional inputs. Models with separable exponential covariance structures are studied. The retrospective designs are constructed by adding or deleting points from an already existing design. The best possible designs are found by minimizing the supremum of mean squared prediction error. Deterministic algorithms are developed to find the best possible retrospective designs. We develop the notion of evenness of two-dimensional grid designs to compare them with each other, using the concept of majorization. For the case of the addition of points, we develop two methods for finding the best possible design, one is adding one point at a time and the other is adding all the points simultaneously. For the case of deletion of the points, we develop the method for deleting all points simultaneously. The results show, that a more evenly spread design is the best possible design and is close to regularly spaced grid designs in terms of their efficiencies. To address the scenarios where covariance parameters are unknown, a pseudo-Bayesian technique is used to determine the best possible designs.
  Keywords: Kriging, G-optimality, grid designs, retrospective designs, regularly spaced grids, separable covariance, Ornstein-Uhlenbeck process.