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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.

Wetland impacts in the Mid-Atlantic USA are frequently mitigated via wetland creation in former uplands. Regulatory approval requires a site-specific water budget that predicts the annual water level regime (hydroperiod). However, many studies of created wetlands indicate that post-construction hydroperiods frequently are not similar to impacted wetland systems. My primary objective was to evaluate a water budget model, Wetbud (Basic model), through comparison of model output to on-site water level data for two created forested wetlands in Northern Virginia. Initial sensitivity analyses indicated that watershed curve number and outlet height had the most leverage on model output. Addition of maximum depth of water level drawdown greatly improved model accuracy. I used Nash-Sutcliffe efficiency (NSE) and root mean squared error (RMSE) to evaluate goodness of fit of model output against site monitoring data. The Basic model reproduced the overall seasonal hydroperiod well once fully parameterized, despite NSE values ranging from -0.67 to 0.41 in calibration and from -4.82 to -0.26 during validation. For RMSE, calibration values ranged from 5.9 cm to 12.7 cm during calibration and from 8.2 cm to 18.5 cm during validation. My second objective was to select a group of "design target hydroperiods" for common Mid-Atlantic USA wetland types. From > 90 sites evaluated, I chose four mineral flats, three riverine wetlands, and one depressional wetland that met all selection criteria. Taken together, improved wetland water budget modeling procedures (like Wetbud) combined with the use of appropriate target hydroperiod information should improve the success of wetland creation efforts. / Master of Science / Wetlands in the USA are defined by the combined occurrence of wetland hydrology, hydric soils, and hydrophytic vegetation. Wetlands serve to retain floodwater, sediments and nutrients within their landscape. They may serve as a source of local groundwater recharge and are home to many endangered species of plants and animals. Wetland ecosystems are frequently impacted by human activities including road-building and development. These impacts can range from the destruction of a wetland to increased nutrient contributions from storm- or wastewater. One commonly utilized option to mitigate wetland impacts is via wetland creation in former upland areas. Regulatory approval requires a site-specific water budget that predicts the average monthly water levels (hydroperiod). A hydroperiod is simply a depiction of how the elevation of water changes over time. However, many studies of created wetlands indicate that post-construction hydroperiods frequently are not representative of the impacted wetland systems. Many software packages, called models, seek to predict the hydroperiod for different wetland systems. Improving and vetting these models help to improve our understanding of how these systems function. My primary objective was to evaluate a water budget model, Wetbud (Basic model), through comparison of model output to onsite water level data for two created forested wetlands in Northern Virginia. Initial analyses indicated that watershed curve number (CN) and outlet height had the most influence on model output. Addition of a maximum depth of water level drawdown below the ground surface greatly improved model accuracy. I used statistical analyses to compare model output to site monitoring data. The Basic model reproduced the overall seasonal hydroperiod well once inputs were set to optimum values (calibration). Statistical results for the calibration varied between excellent and acceptable for our selected measure of accuracy, the root mean squared error. My second objective was to select a grouping of “design target hydroperiods” for common Mid-Atlantic USA wetland types. From > 90 sites evaluated, I chose four mineral flats, three riverine wetlands, and one depressional wetland that met all selection criteria. Taken together, improved wetland water budget modeling procedures (like Wetbud) combined with the use of appropriate target hydroperiod information should improve the success of wetland creation efforts.

It is a common practice when designing a system to apply safety factors to the critical failure load or event. These safety factors provide a buffer against failure due to the random or un-modeled behavior, which may lead the system to exceed these limits. However these safety factors are not directly related to the likelihood of a failure event occurring. If the safety factors are poorly chosen, the system may fail unexpectedly or it may have a design which is too conservative. Reliability-Based Design Optimization (RBDO) is an alternative approach which directly considers the likelihood of failure by incorporating a reliability analysis step such as the First-Order Reliability Method (FORM). The FORM analysis requires the solution of an optimization problem however, so implementing this approach into an RBDO routine creates a double-loop optimization structure. For large problems such as Reliability-Based Topology Optimization (RBTO), numeric sensitivity analysis becomes computationally intractable. In this thesis, a general approach to the sensitivity analysis of nested functions is developed from the Lagrange Multiplier Theorem and then applied to several Reliability-Based Design Optimization problems, including topology optimization. The proposed approach is computationally efficient, requiring only a single solution of the FORM problem each iteration. / Master of Science

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.