http://hdl.handle.net/10256/637 2025-07-02T02:55:34Z 2025-07-02T02:55:34Z Atkinson, A.C. http://hdl.handle.net/10256/753 2022-07-13T06:59:26Z 2008-05-30T00:00:00Z

Experimental design on the simplex Atkinson, A.C. Martín Fernández, Josep Antoni; Daunis-i-Estadella, Pepus Optimum experimental designs depend on the design criterion, the model and the design region. The talk will consider the design of experiments for regression models in which there is a single response with the explanatory variables lying in a simplex. One example is experiments on various compositions of glass such as those considered by Martin, Bursnall, and Stillman (2001). Because of the highly symmetric nature of the simplex, the class of models that are of interest, typically Scheff´e polynomials (Scheff´e 1958) are rather different from those of standard regression analysis. The optimum designs are also rather different, inheriting a high degree of symmetry from the models. In the talk I will hope to discuss a variety of modes for such experiments. Then I will discuss constrained mixture experiments, when not all the simplex is available for experimentation. Other important aspects include mixture experiments with extra non-mixture factors and the blocking of mixture experiments. Much of the material is in Chapter 16 of Atkinson, Donev, and Tobias (2007). If time and my research allows, I would hope to finish with a few comments on design when the responses, rather than the explanatory variables, lie in a simplex. References Atkinson, A. C., A. N. Donev, and R. D. Tobias (2007). Optimum Experimental Designs, with SAS. Oxford: Oxford University Press. Martin, R. J., M. C. Bursnall, and E. C. Stillman (2001). Further results on optimal and efficient designs for constrained mixture experiments. In A. C. Atkinson, B. Bogacka, and A. Zhigljavsky (Eds.), Optimal Design 2000, pp. 225–239. Dordrecht: Kluwer. Scheff´e, H. (1958). Experiments with mixtures. Journal of the Royal Statistical Society, Ser. B 20, 344–360. 1

2008-05-30T00:00:00Z Liebscher, Volkmar http://hdl.handle.net/10256/732 2022-07-13T06:59:26Z 2008-05-28T00:00:00Z

Compositions in life science data Liebscher, Volkmar Daunis-i-Estadella, Pepus; Martín Fernández, Josep Antoni The aim of this talk is to convince the reader that there are a lot of interesting statistical problems in presentday life science data analysis which seem ultimately connected with compositional statistics. Key words: SAGE, cDNA microarrays, (1D-)NMR, virus quasispecies

2008-05-28T00:00:00Z Aitchison, John http://hdl.handle.net/10256/706 2024-09-24T07:06:55Z 2008-05-27T00:00:00Z

The single principle of compositional data analysis, continuing fallacies, confusions and misunderstandings and some suggested remedies Aitchison, John In any discipline, where uncertainty and variability are present, it is important to have principles which are accepted as inviolate and which should therefore drive statistical modelling, statistical analysis of data and any inferences from such an analysis. Despite the fact that two such principles have existed over the last two decades and from these a sensible, meaningful methodology has been developed for the statistical analysis of compositional data, the application of inappropriate and/or meaningless methods persists in many areas of application. This paper identifies at least ten common fallacies and confusions in compositional data analysis with illustrative examples and provides readers with necessary, and hopefully sufficient, arguments to persuade the culprits why and how they should amend their ways

2008-05-27T00:00:00Z