Title: Echelon designs, Hilbert series and Smolyak grids
Authors: Hugo Maruri - QMUL (United Kingdom) [presenting]
Henry Wynn - London School of Economics (United Kingdom)
Abstract: Echelon designs were first described in 2000. These designs are defined for continuous factors and include, amongst others, factorial designs. They have the appealing property that the saturated polynomial model associated with it mirrors the geometric configuration of the design. Perhaps surprisingly, the interpolators for such designs are based upon the Hilbert series of the monomial ideal associated with the polynomial model and thus the interpolators satisfy properties of inclusion-exclusion. Echelon designs are quite flexible for modelling and include the recently developed designs known as Smolyak sparse grids. We present the designs, describe their properties and show examples of application.