11,359 research outputs found
Multi-Attribute Utility Preference Robust Optimization: A Continuous Piecewise Linear Approximation Approach
In this paper, we consider a multi-attribute decision making problem where
the decision maker's (DM's) objective is to maximize the expected utility of
outcomes but the true utility function which captures the DM's risk preference
is ambiguous. We propose a maximin multi-attribute utility preference robust
optimization (UPRO) model where the optimal decision is based on the worst-case
utility function in an ambiguity set of plausible utility functions constructed
using partially available information such as the DM's specific preferences
between some lotteries. Specifically, we consider a UPRO model with two
attributes, where the DM's risk attitude is multivariate risk-averse and the
ambiguity set is defined by a linear system of inequalities represented by the
Lebesgue-Stieltjes (LS) integrals of the DM's utility functions. To solve the
maximin problem, we propose an explicit piecewise linear approximation (EPLA)
scheme to approximate the DM's true unknown utility so that the inner
minimization problem reduces to a linear program, and we solve the approximate
maximin problem by a derivative-free (Dfree) method. Moreover, by introducing
binary variables to locate the position of the reward function in a family of
simplices, we propose an implicit piecewise linear approximation (IPLA)
representation of the approximate UPRO and solve it using the Dfree method.
Such IPLA technique prompts us to reformulate the approximate UPRO as a single
mixed-integer program (MIP) and extend the tractability of the approximate UPRO
to the multi-attribute case. Furthermore, we extend the model to the expected
utility maximization problem with expected utility constraints where the
worst-case utility functions in the objective and constraints are considered
simultaneously. Finally, we report the numerical results about performances of
the proposed models.Comment: 50 pages,18 figure
Model Diagnostics meets Forecast Evaluation: Goodness-of-Fit, Calibration, and Related Topics
Principled forecast evaluation and model diagnostics are vital in fitting probabilistic models and forecasting outcomes of interest. A common principle is that fitted or predicted distributions ought to be calibrated, ideally in the sense that the outcome is indistinguishable from a random draw from the posited distribution. Much of this thesis is centered on calibration properties of various types of forecasts.
In the first part of the thesis, a simple algorithm for exact multinomial goodness-of-fit tests is proposed. The algorithm computes exact -values based on various test statistics, such as the log-likelihood ratio and Pearson\u27s chi-square. A thorough analysis shows improvement on extant methods. However, the runtime of the algorithm grows exponentially in the number of categories and hence its use is limited.
In the second part, a framework rooted in probability theory is developed, which gives rise to hierarchies of calibration, and applies to both predictive distributions and stand-alone point forecasts. Based on a general notion of conditional T-calibration, the thesis introduces population versions of T-reliability diagrams and revisits a score decomposition into measures of miscalibration, discrimination, and uncertainty. Stable and efficient estimators of T-reliability diagrams and score components arise via nonparametric isotonic regression and the pool-adjacent-violators algorithm. For in-sample model diagnostics, a universal coefficient of determination is introduced that nests and reinterprets the classical in least squares regression.
In the third part, probabilistic top lists are proposed as a novel type of prediction in classification, which bridges the gap between single-class predictions and predictive distributions. The probabilistic top list functional is elicited by strictly consistent evaluation metrics, based on symmetric proper scoring rules, which admit comparison of various types of predictions
Mathematical models to evaluate the impact of increasing serotype coverage in pneumococcal conjugate vaccines
Of over 100 serotypes of Streptococcus pneumoniae, only 7 were included in the first pneumo- coccal conjugate vaccine (PCV). While PCV reduced the disease incidence, in part because of a herd immunity effect, a replacement effect was observed whereby disease was increasingly caused by serotypes not included in the vaccine. Dynamic transmission models can account for these effects to describe post-vaccination scenarios, whereas economic evaluations can enable decision-makers to compare vaccines of increasing valency for implementation. This thesis has four aims. First, to explore the limitations and assumptions of published pneu- mococcal models and the implications for future vaccine formulation and policy. Second, to conduct a trend analysis assembling all the available evidence for serotype replacement in Europe, North America and Australia to characterise invasive pneumococcal disease (IPD) caused by vaccine-type (VT) and non-vaccine-types (NVT) serotypes. The motivation behind this is to assess the patterns of relative abundance in IPD cases pre- and post-vaccination, to examine country-level differences in relation to the vaccines employed over time since introduction, and to assess the growth of the replacement serotypes in comparison with the serotypes targeted by the vaccine. The third aim is to use a Bayesian framework to estimate serotype-specific invasiveness, i.e. the rate of invasive disease given carriage. This is useful for dynamic transmission modelling, as transmission is through carriage but a majority of serotype-specific pneumococcal data lies in active disease surveillance. This is also helpful to address whether serotype replacement reflects serotypes that are more invasive or whether serotypes in a specific location are equally more invasive than in other locations. Finally, the last aim of this thesis is to estimate the epidemiological and economic impact of increas- ing serotype coverage in PCVs using a dynamic transmission model. Together, the results highlight that though there are key parameter uncertainties that merit further exploration, divergence in serotype replacement and inconsistencies in invasiveness on a country-level may make a universal PCV suboptimal.Open Acces
Limit theorems for non-Markovian and fractional processes
This thesis examines various non-Markovian and fractional processes---rough volatility models, stochastic Volterra equations, Wiener chaos expansions---through the prism of asymptotic analysis.
Stochastic Volterra systems serve as a conducive framework encompassing most rough volatility models used in mathematical finance. In Chapter 2, we provide a unified treatment of pathwise large and moderate deviations principles for a general class of multidimensional stochastic Volterra equations with singular kernels, not necessarily of convolution form. Our methodology is based on the weak convergence approach by Budhiraja, Dupuis and Ellis.
This powerful approach also enables us to investigate the pathwise large deviations of families of white noise functionals characterised by their Wiener chaos expansion as~
In Chapter 3, we provide sufficient conditions for the large deviations principle to hold in path space, thereby refreshing a problem left open By Pérez-Abreu (1993). Hinging on analysis on Wiener space, the proof involves describing, controlling and identifying the limit of perturbed multiple stochastic integrals.
In Chapter 4, we come back to mathematical finance via the route of Malliavin calculus. We present explicit small-time formulae for the at-the-money implied volatility, skew and curvature in a large class of models, including rough volatility models and their multi-factor versions. Our general setup encompasses both European options on a stock and VIX options. In particular, we develop a detailed analysis of the two-factor rough Bergomi model.
Finally, in Chapter 5, we consider the large-time behaviour of affine stochastic Volterra equations, an under-developed area in the absence of Markovianity.
We leverage on a measure-valued Markovian lift introduced by Cuchiero and Teichmann and the associated notion of generalised Feller property.
This setting allows us to prove the existence of an invariant measure for the lift and hence of a stationary distribution for the affine Volterra process, featuring in the rough Heston model.Open Acces
Discovering the hidden structure of financial markets through bayesian modelling
Understanding what is driving the price of a financial asset is a question that is currently mostly unanswered. In this work we go beyond the classic one step ahead prediction and instead construct models that create new information on the behaviour of these time series. Our aim is to get a better understanding of the hidden structures that drive the moves of each financial time series and thus the market as a whole.
We propose a tool to decompose multiple time series into economically-meaningful variables to explain the endogenous and exogenous factors driving their underlying variability. The methodology we introduce goes beyond the direct model forecast. Indeed, since our model continuously adapts its variables and coefficients, we can study the time series of coefficients and selected variables. We also present a model to construct the causal graph of relations between these time series and include them in the exogenous factors.
Hence, we obtain a model able to explain what is driving the move of both each specific time series and the market as a whole. In addition, the obtained graph of the time series provides new information on the underlying risk structure of this environment. With this deeper understanding of the hidden structure we propose novel ways to detect and forecast risks in the market. We investigate our results with inferences up to one month into the future using stocks, FX futures and ETF futures, demonstrating its superior performance according to accuracy of large moves, longer-term prediction and consistency over time. We also go in more details on the economic interpretation of the new variables and discuss the created graph structure of the market.Open Acces
Fiabilité de l’underfill et estimation de la durée de vie d’assemblages microélectroniques
Abstract : In order to protect the interconnections in flip-chip packages, an underfill material layer
is used to fill the volumes and provide mechanical support between the silicon chip and
the substrate. Due to the chip corner geometry and the mismatch of coefficient of thermal
expansion (CTE), the underfill suffers from a stress concentration at the chip corners when
the temperature is lower than the curing temperature. This stress concentration leads
to subsequent mechanical failures in flip-chip packages, such as chip-underfill interfacial
delamination and underfill cracking. Local stresses and strains are the most important
parameters for understanding the mechanism of underfill failures. As a result, the industry
currently relies on the finite element method (FEM) to calculate the stress components, but
the FEM may not be accurate enough compared to the actual stresses in underfill. FEM
simulations require a careful consideration of important geometrical details and material
properties. This thesis proposes a modeling approach that can accurately estimate the underfill delamination
areas and crack trajectories, with the following three objectives. The first
objective was to develop an experimental technique capable of measuring underfill deformations
around the chip corner region. This technique combined confocal microscopy and
the digital image correlation (DIC) method to enable tri-dimensional strain measurements
at different temperatures, and was named the confocal-DIC technique. This techique was
first validated by a theoretical analysis on thermal strains. In a test component similar
to a flip-chip package, the strain distribution obtained by the FEM model was in good
agreement with the results measured by the confocal-DIC technique, with relative errors
less than 20% at chip corners. Then, the second objective was to measure the strain near
a crack in underfills. Artificial cracks with lengths of 160 μm and 640 μm were fabricated
from the chip corner along the 45° diagonal direction. The confocal-DIC-measured
maximum hoop strains and first principal strains were located at the crack front area for
both the 160 μm and 640 μm cracks. A crack model was developed using the extended
finite element method (XFEM), and the strain distribution in the simulation had the same
trend as the experimental results. The distribution of hoop strains were in good agreement
with the measured values, when the model element size was smaller than 22 μm to
capture the strong strain gradient near the crack tip. The third objective was to propose
a modeling approach for underfill delamination and cracking with the effects of manufacturing
variables. A deep thermal cycling test was performed on 13 test cells to obtain the
reference chip-underfill delamination areas and crack profiles. An artificial neural network
(ANN) was trained to relate the effects of manufacturing variables and the number of
cycles to first delamination of each cell. The predicted numbers of cycles for all 6 cells in
the test dataset were located in the intervals of experimental observations. The growth
of delamination was carried out on FEM by evaluating the strain energy amplitude at
the interface elements between the chip and underfill. For 5 out of 6 cells in validation,
the delamination growth model was consistent with the experimental observations. The
cracks in bulk underfill were modelled by XFEM without predefined paths. The directions of edge cracks were in good agreement with the experimental observations, with an error
of less than 2.5°. This approach met the goal of the thesis of estimating the underfill
initial delamination, areas of delamination and crack paths in actual industrial flip-chip
assemblies.Afin de protéger les interconnexions dans les assemblages, une couche de matériau d’underfill est utilisée pour remplir le volume et fournir un support mécanique entre la puce de silicium et le substrat. En raison de la géométrie du coin de puce et de l’écart du coefficient de dilatation thermique (CTE), l’underfill souffre d’une concentration de contraintes dans les coins lorsque la température est inférieure à la température de cuisson. Cette concentration de contraintes conduit à des défaillances mécaniques dans les encapsulations de flip-chip, telles que la délamination interfaciale puce-underfill et la fissuration d’underfill. Les contraintes et déformations locales sont les paramètres les plus importants pour comprendre le mécanisme des ruptures de l’underfill. En conséquent, l’industrie utilise actuellement la méthode des éléments finis (EF) pour calculer les composantes de la contrainte, qui ne sont pas assez précises par rapport aux contraintes actuelles dans l’underfill. Ces simulations nécessitent un examen minutieux de détails géométriques importants et des propriétés des matériaux. Cette thèse vise à proposer une approche de modélisation permettant d’estimer avec précision les zones de délamination et les trajectoires des fissures dans l’underfill, avec les trois objectifs suivants. Le premier objectif est de mettre au point une technique expérimentale capable de mesurer la déformation de l’underfill dans la région du coin de puce. Cette technique, combine la microscopie confocale et la méthode de corrélation des images numériques (DIC) pour permettre des mesures tridimensionnelles des déformations à différentes températures, et a été nommée le technique confocale-DIC. Cette technique a d’abord été validée par une analyse théorique en déformation thermique. Dans un échantillon similaire à un flip-chip, la distribution de la déformation obtenues par le modèle EF était en bon accord avec les résultats de la technique confocal-DIC, avec des erreurs relatives inférieures à 20% au coin de puce. Ensuite, le second objectif est de mesurer la déformation autour d’une fissure dans l’underfill. Des fissures artificielles d’une longueuer de 160 μm et 640 μm ont été fabriquées dans l’underfill vers la direction diagonale de 45°. Les déformations circonférentielles maximales et principale maximale étaient situées aux pointes des fissures correspondantes. Un modèle de fissure a été développé en utilisant la méthode des éléments finis étendue (XFEM), et la distribution des contraintes dans la simuation a montré la même tendance que les résultats expérimentaux. La distribution des déformations circonférentielles maximales était en bon accord avec les valeurs mesurées lorsque la taille des éléments était plus petite que 22 μm, assez petit pour capturer le grand gradient de déformation près de la pointe de fissure. Le troisième objectif était d’apporter une approche de modélisation de la délamination et de la fissuration de l’underfill avec les effets des variables de fabrication. Un test de cyclage thermique a d’abord été effectué sur 13 cellules pour obtenir les zones délaminées entre la puce et l’underfill, et les profils de fissures dans l’underfill, comme référence. Un réseau neuronal artificiel (ANN) a été formé pour établir une liaison entre les effets des variables de fabrication et le nombre de cycles à la délamination pour chaque cellule. Les nombres de cycles prédits pour les 6 cellules de l’ensemble de test étaient situés dans les intervalles d’observations expérimentaux. La croissance de la délamination a été réalisée par l’EF en évaluant l’énergie de la déformation au niveau des éléments interfaciaux entre la puce et l’underfill. Pour 5 des 6 cellules de la validation, le modèle de croissance du délaminage était conforme aux observations expérimentales. Les fissures dans l’underfill ont été modélisées par XFEM sans chemins prédéfinis. Les directions des fissures de bord étaient en bon accord avec les observations expérimentales, avec une erreur inférieure à 2,5°. Cette approche a répondu à la problématique qui consiste à estimer l’initiation des délamination, les zones de délamination et les trajectoires de fissures dans l’underfill pour des flip-chips industriels
Flood Inflow Forecast Using L2-norm Ensemble Weighting Sea Surface Feature
It is important to forecast dam inflow for flood damage mitigation. The
hydrograph provides critical information such as the start time, peak level,
and volume. Particularly, dam management requires a 6-h lead time of the dam
inflow forecast based on a future hydrograph. The authors propose novel target
inflow weights to create an ocean feature vector extracted from the analyzed
images of the sea surface. We extracted 4,096 elements of the dimension vector
in the fc6 layer of the pre-trained VGG16 network. Subsequently, we reduced it
to three dimensions of t-SNE. Furthermore, we created the principal component
of the sea temperature weights using PCA. We found that these weights
contribute to the stability of predictor importance by numerical experiments.
As base regression models, we calibrate the least squares with kernel
expansion, the quantile random forest minimized out-of bag error, and the
support vector regression with a polynomial kernel. When we compute the
predictor importance, we visualize the stability of each variable importance
introduced by our proposed weights, compared with other results without
weights. We apply our method to a dam at Kanto region in Japan and focus on the
trained term from 2007 to 2018, with a limited flood term from June to October.
We test the accuracy over the 2019 flood term. Finally, we present the applied
results and further statistical learning for unknown flood forecast.Comment: 23 pages, 13 figures, 5 table
Graphical scaffolding for the learning of data wrangling APIs
In order for students across the sciences to avail themselves of modern data streams, they must first know how to wrangle data: how to reshape ill-organised, tabular data into another format, and how to do this programmatically, in languages such as Python and R. Despite the cross-departmental demand and the ubiquity of data wrangling in analytical workflows, the research on how to optimise the instruction of it has been minimal. Although data wrangling as a programming domain presents distinctive challenges - characterised by on-the-fly syntax lookup and code example integration - it also presents opportunities. One such opportunity is how tabular data structures are easily visualised. To leverage the inherent visualisability of data wrangling, this dissertation evaluates three types of graphics that could be employed as scaffolding for novices: subgoal graphics, thumbnail graphics, and parameter graphics. Using a specially built e-learning platform, this dissertation documents a multi-institutional, randomised, and controlled experiment that investigates the pedagogical effects of these. Our results indicate that the graphics are well-received, that subgoal graphics boost the completion rate, and that thumbnail graphics improve navigability within a command menu. We also obtained several non-significant results, and indications that parameter graphics are counter-productive. We will discuss these findings in the context of general scaffolding dilemmas, and how they fit into a wider research programme on data wrangling instruction
- …