Inference of distributional parameters from compositional samples containing nondetects

Low concentrations of elements in geochemical analyses have the peculiarity of being compositional data and, for a given level of significance, are likely to be beyond the capabilities of laboratories to distinguish between minute concentrations and complete absence, thus preventing laboratories from reporting extremely low concentrations of the analyte. Instead, what is reported is the detection limit, which is the minimum concentration that conclusively differentiates between presence and absence of the element. A spatially distributed exhaustive sample is employed in this study to generate unbiased sub-samples, which are further censored to observe the effect that different detection limits and sample sizes have on the inference of population distributions starting from geochemical analyses having specimens below detection limit (nondetects). The isometric logratio transformation is used to convert the compositional data in the simplex to samples in real space, thus allowing the practitioner to properly borrow from the large source of statistical techniques valid only in real space. The bootstrap method is used to numerically investigate the reliability of inferring several distributional parameters employing different forms of imputation for the censored data. The case study illustrates that, in general, best results are obtained when imputations are made using the distribution best fitting the readings above detection limit and exposes the problems of other more widely used practices. When the sample is spatially correlated, it is necessary to combine the bootstrap with stochastic simulation

Prediction of glucose excursions under uncertain parameters and food intake in intensive insulin therapy for type 1 diabetes mellitus

Considering the difficulty in the insulin dosage selection and the problem of hyper- and hypoglycaemia episodes in type 1 diabetes, dosage-aid systems appear as tremendously helpful for these patients. A model-based approach to this problem must unavoidably consider uncertainty sources such as the large intra-patient variability and food intake. This work addresses the prediction of glycaemia for a given insulin therapy face to parametric and input uncertainty, by means of modal interval analysis. As result, a band containing all possible glucose excursions suffered by the patient for the given uncertainty is obtained. From it, a safer prediction of possible hyper- and hypoglycaemia episodes can be calculated

Application of modal interval analysis to the simulation of the behaviour of dynamic systems with uncertain parameters

Els models matemàtics quantitatius són simplificacions de la realitat i per tant el comportament obtingut per simulació d'aquests models difereix dels reals. L'ús de models quantitatius complexes no és una solució perquè en la majoria dels casos hi ha alguna incertesa en el sistema real que no pot ser representada amb aquests models. Una forma de representar aquesta incertesa és mitjançant models qualitatius o semiqualitatius. Un model d'aquest tipus de fet representa un conjunt de models. La simulació del comportament de models quantitatius genera una trajectòria en el temps per a cada variable de sortida. Aquest no pot ser el resultat de la simulació d'un conjunt de models. Una forma de representar el comportament en aquest cas és mitjançant envolupants. L'envolupant exacta és complete, és a dir, inclou tots els possibles comportaments del model, i correcta, és a dir, tots els punts dins de l'envolupant pertanyen a la sortida de, com a mínim, una instància del model. La generació d'una envolupant així normalment és una tasca molt dura que es pot abordar, per exemple, mitjançant algorismes d'optimització global o comprovació de consistència. Per aquesta raó, en molts casos s'obtenen aproximacions a l'envolupant exacta. Una aproximació completa però no correcta a l'envolupant exacta és una envolupant sobredimensionada, mentre que una envolupant correcta però no completa és subdimensionada. Aquestes propietats s'han estudiat per diferents simuladors per a sistemes incerts.