Title: On numerical fans for noisy experimental designs
Authors: Arkadius Kalka - Dortmund University of Applied Sciences and Arts (Germany) [presenting]
Abstract: Identifiability of models is an important issue in experimental design. The theory of Groebner basis and algebraic fans has been applied to this subject. In the case of noisy designs, e.g., when the design points themselves are observations, some models are only identifiable due to small deviations of the design. In order to avoid such unstable models, the notion of numerical algebraic fan has been developed which deploys the numerical Buchberger algorithm. We compare the numerical algebraic fan with other possible notions of numerical fans, in particular more straightforward methods which we call the numerical statistical fan. A model lies in the numerical statistical fan if its design matrix is approximatively of full rank, otherwise the columns of its design matrix are approximate linear dependent. Given some small precision parameter $\epsilon >0$, $n$ vectors may be defined as approximate (or almost) linear dependent if there exists an $(n-1)$-dimensional subspace such that the sum of distances (squared) of the points to the subspace is smaller than $\epsilon$. Data from a thermal spraying process is used to compare the goodness of fit of models coming from different approaches.