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Background: A pilot study can be an important step in the assessment of an intervention by providing information to design the future definitive trial. Pilot studies can be used to estimate the recruitment and retention rates and population variance and to provide preliminary evidence of efficacy potential. However, estimation is poor because pilot studies are small, so sensitivity analyses for the main trial's sample size calculations should be undertaken. Methods: We demonstrate how to carry out easy-to-perform sensitivity analysis for designing trials based on pilot data using an example. Furthermore, we introduce rules of thumb for the size of the pilot study so that the overall sample size, for both pilot and main trials, is minimized. Results: The example illustrates how sample size estimates for the main trial can alter dramatically by plausibly varying assumptions. Required sample size for 90% power varied from 392 to 692 depending on assumptions. Some scenarios were not feasible based on the pilot study recruitment and retention rates. Conclusion: Pilot studies can be used to help design the main trial, but caution should be exercised. We recommend the use of sensitivity analyses to assess the robustness of the design assumptions for a main trial.

The following thesis is focused on the use of Monte Carlo simulation in business valuation. It examines the theoretical context of the valuation process and simulation techniques and subsequently applies these to the valuation of Plzeňský Prazdroj, a. s. as of 31.3.2008. The aim was to explore the potential of application of Monte Carlo simulation and to interpret obtained information. There was created the valuation model and performed sensitivity analysis based on which there were identified factors which have significant impact on the value. These were further investigated and characterized in terms of probability. Following the extension of the model to include uncertainty factors there was simulated business value in relation to the variability of uncertainty factors and the result was subsequently interpreted. It was concluded that Monte Carlo simulation may be useful predominantly in search for subjective value for investor due to additional information obtained.

The Malliavin-Thalmaier formula was introduced for simulation of high dimensional probability density functions. But when this integration by parts formula is applied directly in computer simulations, we show that it is unstable. We propose an approximation to the Malliavin-Thalmaier formula. In this paper, we find the order of the bias and the variance of the approximation error. And we obtain an explicit Malliavin-Thalmaier formula for the calculation of Greeks in finance. The weights obtained are free from the curse of dimensionality.

[EN] The present Ph.D. Thesis considers epidemiological mathematical models based on ordinary differential equations and shows its application to understand the cocaine consumption epidemic in Spain. Three mathematical models are presented to predict the evolution of the epidemic in the near future in order to select the model that best reflects the data. By the results obtained for the selected model, if there are not changes in cocaine consumption policies or in the economic environment, the cocaine consumption will increase in Spain over the next few years. Furthermore, we use different techniques to estimate 95% confidence intervals and, consequently, quantify the uncertainty in the predictions. In addition, using several techniques, we conducted a model sensitivity analysis to determine which parameters are those that most influence the cocaine consumption in Spain. These analysis reveal that prevention actions on cocaine consumer population can be the most effective strategy to control this trend. / [ES] La presente Tesis considera modelos matemáticos epidemiológicos basados en ecuaciones diferenciales ordinarias y muestra su aplicación para entender la epidemia del consumo de cocaína en España. Se presentan tres modelos matemáticos para predecir la evolución de dicha epidemia en un futuro próximo, con el objetivo de seleccionar el modelo que mejor refleja los datos. Por los resultados obtenidos para el modelo seleccionado, si no hay cambios en las políticas del consumo de cocaína ni en el ámbito económico, el consumo de cocaína aumentará en los próximos años. Además, utilizamos diferentes técnicas para estimar los intervalos de confianza al 95% y, de esta forma, cuantificar la incertidumbre en las predicciones. Finalmente, utilizando diferentes técnicas, hemos realizado un análisis de sensibilidad para determinar qué parámetros son los que más influyen en el consumo de cocaína. Estos análisis revelan que las acciones de prevención sobre la población de consumidores de cocaína pueden ser la estrategia más efectiva para controlar esta tendencia. / [CAT] La present Tesi considera models matemàtics epidemiològics basats en equacions diferencials ordinàries i mostra la seua aplicació per a entendre l'epidèmia del consum de cocaïna en Espanya. Es presenten tres models matemàtics per a predir l'evolució d'aquesta epidèmia en un futur pròxim, amb l'objectiu de seleccionar el model que millor reflecteix les dades. Pels resultats obtinguts per al model seleccionat, si no hi ha canvis en les polítiques de consum de cocaïna ni en l'àmbit econòmic, el consum de cocaïna augmentarà en els pròxims anys. A més, utilitzem diferents tècniques per a estimar els intervals de confiança al 95% i, d'aquesta manera, quantificar la incertesa en les prediccions. Finalment, utilitzant diferents tècniques, hem realitzat un anàlisi de sensibilitat per a determinar quins paràmetres són els que més influencien el consum de cocaïna. Aquestos anàlisis revelen que les accions de prevenció en la població de consumidors de cocaïna poden ser l'estratègia més efectiva per a controlar aquesta tendència. / Rubio Monzó, M. (2015). Uncertainty quantification in dynamical models. An application to cocaine consumption in Spain [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/55844 / TESIS

Nowadays, as oil industry gradually moves towards deep sea fields with water depth more than 1000 meters, they are subjected to several threats which can cause failure of the pipeline, of which the accidentally-dropped objects have become the leading external risk factor for subsea developments. In this thesis, a sample field layout introduced in Det Norske Veritas (DNV) guide rules is selected as the study case with 100 m water depth. Six different groups of dropped objects are used in this paper. The conditional hit probability for long/flat shaped objects will be calculated with the methods from both DNV rules and an in-house tool Dropped Objects Simulator (DROBS). The difference between the results will be discussed. Meanwhile, the sensitivity analysis on mass, collision area , the volume, added mass coefficient and drag coefficient of the objects are calculated.

Les aquifères karstiques sont associés à des enjeux importants en termes à la fois de gestion de la ressource en eau et de gestion du risque d'inondation. Ces systèmes sont caractérisés par une structure fortement hétérogène et un fonctionnement non-linéaire. Cette thèse est consacrée à l'étude de la sensibilité et de l'incertitude associés à la modélisation numérique des écoulements en milieu karstique. De façon systématique, l'analyse de sensibilité est utilisée comme outil afin de répondre aux questions suivantes: (i) la calibration est-elle possible ? (ii) la calibration est-elle robuste ? (iii) est-il possible de réduire l'équifinalité via une calibration multi-objectif ou multi-variable ?Cette contribution met en évidence le potentiel des méthodes locales d'analyse de sensibilité. En dépit des limitations inhérentes à cette approche (approximation locale et perturbation d'un facteur à la fois), l'analyse locale permet une compréhension fine du fonctionnement du modèle, pour un coût de calcul réduit.Par ailleurs, cet travail souligne l'intérêt d'une calibration multi-variable par rapport à une calibration multi-objectif, dans une optique de réduction de l'équifinalité / Karst aquifers are associated with key issues for water resource management and also for flood risk mitigation. These systems are characterized by a highly heterogeneous structure and non-linear functioning. This thesis addresses the sensitivity and uncertainty associated with the numerical modelling of groundwater flow in karst systems. As a systematic approach, sensitivity analysis has been used to answer the following questions:(i) is it possible to calibrate the model ? (ii) is the calibration robust ? (iii) is it possible to reduce equifinality, through multi-objective calibration or through multi-variable calibration ? This contribution stresses the potentialities of local sensitivity analyses. Despite their inherent limitations (local approximation), local analyses have proved to bring valuable insights into the general behaviour of complex, non-linear flow models, at little computational cost. Besides, this contribution also stresses the interest of multi-variable calibration as compared to multi-objective calibration, as regards equifinality reduction.

Ignition delay time, τ_ign, is a key quantity of interest that is used to assess the predictability of a chemical kinetic model. This dissertation explores the sensitivity of τ_ign to uncertainties in: 1. rate-rule kinetic rates parameters and 2. enthalpies and entropies of fuel and fuel radicals using global and local sensitivity approaches. We begin by considering variability in τ_ign to uncertainty in rate parameters. We consider a 30-dimensional stochastic germ in which each random variable is associated with one reaction class, and build a surrogate model for τ_ign using polynomial chaos expansions. The adaptive pseudo-spectral projection technique is used for this purpose. First-order and total-order sensitivity indices characterizing the dependence of τ_ign on uncertain inputs are estimated. Results indicate that τ_ign is mostly sensitive to variations in four dominant reaction classes. Next, we develop a thermodynamic class approach to study variability in τ_ign of n-butanol due to uncertainty in thermodynamic properties of species of interest, and to define associated uncertainty ranges. A global sensitivity analysis is performed, again using surrogates constructed using an adaptive pseudo-spectral method. Results indicate that the variability of τ_ign is dominated by uncertainties in the classes associated with peroxy and hydroperoxide radicals. We also perform a combined sensitivity analysis of uncertainty in kinetic rates and thermodynamic properties which revealed that uncertainties in thermodynamic properties can induce variabilities in ignition delay time that are as large as those associated with kinetic rate uncertainties. In the last part, we develop a tangent linear approximation (TLA) to estimate the sensitivity of τ_ign with respect to individual rate parameters and thermodynamic properties in detailed chemical mechanisms. Attention is focused on a gas mixture reacting under adiabatic, constant-volume conditions. The proposed approach is based on integrating the linearized system of equations governing the evolution of the partial derivatives of the state vector with respect to individual random variables, and a linearized approximation is developed to relate ignition delay sensitivity to scaled partial derivatives of temperature. The computations indicate that TLA leads to robust local sensitivity predictions at a computational cost that is order-of-magnitude smaller than that incurred by finite-difference approaches.

As a result of the global climate change, extreme precipitation is occurring more frequently which increases the risk of flooding, especially in urban areas. Urbanisation is widely discussed regarding urban flooding where an increase of impervious surfaces limits the infiltration and increases the surface runoff. Flooding events in urban areas are increasing around the world and can cause large damages on infrastructure and buildings, which makes the cities vulnerable. Urban flood models are an important tool for analysing the capacity of the drainage systems, to predict the extent of the events and to find optimal locations to implement measures to prevent damages from flooding. In this project, a sensitivity analysis in MIKE FLOOD, a coupled 1D-2D flood model developed by DHI is presented, where sewer- and surface systems are integrated. The aim with this project is to investigate how the result of a coupled flood model vary in relation to changes in input parameters. The sensitivity analysis is performed to evaluate how different parameters impact the model output in terms of water depth and variations in cost of flooded buildings, roads, rail- and tramways. The analysis is applied in a case study in Lundby-Lindholmen, Gothenburg city, Sweden. The results show that modelling without infiltration influenced the model output the most, with the largest increase both in terms of cost and water depth over the investigated area. Here the correlation between the initial water saturation and location of the applied pre-rain was highlighted. The model outputs were less sensitive to changes in surface roughness (expressed as Manning value) than without infiltration but did lead to measurable changes in surface water depth and distribution while the flood damage cost didn’t show any major changes. Additionally, the coupled flood model was evaluated in terms of handling changes in magnitudes of rain-events. Data indicates the shorter the return period, the smaller the flood propagation, as well as the flood damage cost decreases with shorter return periods. The data evaluated supports the use of this coupled model approach for shorter return periods in terms of flood propagation.