Invited sessionhttp://hdl.handle.net/10256/6372016-07-01T21:38:56Z2016-07-01T21:38:56ZExperimental design on the simplexAtkinson, A.C.http://hdl.handle.net/10256/7532013-07-17T09:56:48Z2008-05-30T00:00:00ZExperimental design on the simplex
Atkinson, A.C.
Martín Fernández, Josep Antoni; Daunis i Estadella, Josep
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
2008-05-30T00:00:00ZCompositions in life science dataLiebscher, Volkmarhttp://hdl.handle.net/10256/7322013-07-17T09:57:13Z2008-05-28T00:00:00ZCompositions in life science data
Liebscher, Volkmar
Daunis i Estadella, Josep; 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
2008-05-28T00:00:00ZThe single principle of compositional data analysis, continuing fallacies, confusions
and misunderstandings and some suggested remediesAitchison, Johnhttp://hdl.handle.net/10256/7062015-04-09T07:51:35Z2008-05-27T00:00:00ZThe single principle of compositional data analysis, continuing fallacies, confusions
and misunderstandings and some suggested remedies
Aitchison, John
Daunis i Estadella, Josep; Martín Fernández, Josep Antoni
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