1,721,011 research outputs found
Grobner basis methods for structuring and analyzing complex industrial experiments
No full textINTERNATIONAL JOURNAL OF RELIABILITY, QUALITY, AND SAFETY ENGINEERIN
Differential algebra methods for the study of the structural identifiability of rational function state-space models in the biosciences
No full textIn this paper methods from differential algebra are used to study the structural identifiability of biological and pharmacokinetics models expressed in state-space form and with a structure given by rational functions. The focus is on the examples presented and on the application of efficient, automatic methods to test for structural identifiability for various input-output experiments. Differential algebra methods are coupled with Grobner bases, Lie derivatives and the Taylor series expansion in order to obtain efficient algorithms. In particular, an upper bound on the number of derivatives needed for the Taylor series approach for a structural identifiability analysis of rational function models is given. (C) 2001 Elsevier Science Inc. All rights reserved
The application of computational algebraic geometry to the analysis of designed experiments: a case study
No full textStaged trees for discrete longitudinal data
No full textIn this paper we investigate the use of staged tree models for discrete longitudinal data. Staged trees are a type of probabilistic graphical model for finite sample space processes. They are a natural fit for longitudinal data because a temporal ordering is often implicitly assumed and standard methods can be used for model selection and probability estimation. However, model selection methods perform poorly when the sample size is small relative to the size of the graph and model interpretation is tricky with larger graphs. This is exacerbated by longitudinal data which is characterized by repeated observations. To address these issues we propose two approaches: the longitudinal staged tree with Markov assumptions which makes some initial conditional independence assumptions represented by a directed acyclic graph and marginal longitudinal staged trees which model certain margins of the data
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