[Forum SIS] Seminario Prof.ssa Tommasi

[Dip. Scienze Statistiche - Mi]

Il Dipartimento di Scienze Statistiche dell'Università Cattolica del Sacro Cuore ha organizzato un seminario, presentato dalla Prof.ssa Chiara TOMMASI, dell'Università degli Studi di Milano, dal titolo:


An introduction to optimal design of experiments



Venerdì 13 Dicembre dalle ore 11,30

in Aula G 053



Università Cattolica del Sacro Cuore - Milano

Largo Gemelli,1 - Edificio Lanzone 18

Abstract:
Experiments are commonly conducted in many scientific contexts. In this setting the experimenter can freely choose the levels of some experimental conditions X; at each value of X an experiment is run and a response variable Y is observed.
Let the probability distribution of Y (i.e. the statistical model) depend on the experimental conditions and let it be completely known except for some parameters.
The goal of the Theory of Optimum Design is to fix the levels of the experimental conditions and the proportion of observations to be taken at each level, in order to estimate as precisely as possible the unknown parameters of the model. These optimal levels and proportions of observations constitute an optimal design. Optimal designs are computed  minimizing some convex functions (called optimality criteria) of the inverse of the Fisher information matrix. Therefore, an optimal design minimizes (in some sense) the asymptotic covariance matrix of the maximum likelihood estimator. The most popular optimality criterion is the D-criterion, which is the determinant of the inverse of the Fisher information matrix and minimizes the volume of the ellipsoid of concentration of the unknown vector of parameters.
One of the criticisms usually made to the Theory of Optimal Design is that a particular model has to be assumed before designing the experiment, that is before having any data. Sometimes several competing models are adequate for the same problem. In this case, a model has to be chosen after a discrimination hypotheses test. An optimality criterion to discriminate between two homoscedastic models for Normally distributed observations is the T-criterion, which maximizes the power function of the F test for lack of fit. When the rival models are nested and they differ by s parameters, another criterion for model discrimination is the Ds-one. Both T- and Ds-criteria can be applied under specific model assumptions. Differently, the recently proposed KL-criterion may be applied in a very general context: the rival models may be nested or separate; homoscedastic or heteroscedastic; Gaussian or not. The KL-criterion is based on the Kullback-Leibler divergence and it coincides with the T-criterion when the observations are normally distributed.



Segreteria Organizzativa:
Barbara Villa
Dipartimento di Scienze statistiche
Università Cattolica del Sacro Cuore
Largo Gemelli, 1
Edificio Via Lanzone, 18
20123 Milano
Tel. 02/72342647
Fax 02/72343064
e-mail: dip.scienzestatistiche at unicatt.it
http://dipartimenti.unicatt.it/scienze_statistiche


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