Robust Uncertainty Quantification and Scalable Computation for Computer Models with Massive Output

Uncertainty quantification (UQ) is both an old and new concept. The current novelty lies in the interactions and synthesis of mathematical models, computer experiments, statistics, field/real experiments, and probability theory, with a particular emphasize on the large-scale simulations by computer models. The challenges not only come from the complication of scientific questions, but also from the size of the information. It is the focus in this thesis to provide statistical models that are scalable to massive data produced in computer experiments and real experiments, through fast and robust statistical inference.

Chapter 2 provides a practical approach for simultaneously emulating/approximating massive number of functions, with the application on hazard quantification of Soufri\`{e}re Hills volcano in Montserrate island. Chapter 3 discusses another problem with massive data, in which the number of observations of a function is large. An exact algorithm that is linear in time is developed for the problem of interpolation of Methylation levels. Chapter 4 and Chapter 5 are both about the robust inference of the models. Chapter 4 provides a new criteria robustness parameter estimation criteria and several ways of inference have been shown to satisfy such criteria. Chapter 5 develops a new prior that satisfies some more criteria and is thus proposed to use in practice.

Holocene precipitation change in different monsoon sub-regions (time-slices and transient data) simulated by different global climate models, with links to model results

The recently proposed global monsoon hypothesis interprets monsoon systems as part of one global-scale atmospheric overturning circulation, implying a connection between the regional monsoon systems and an in-phase behaviour of all northern hemispheric monsoons on annual timescales (Trenberth et al., 2000). Whether this concept can be applied to past climates and variability on longer timescales is still under debate, because the monsoon systems exhibit different regional characteristics such as different seasonality (i.e. onset, peak, and withdrawal). To investigate the interconnection of different monsoon systems during the pre-industrial Holocene, five transient global climate model simulations have been analysed with respect to the rainfall trend and variability in different sub-domains of the Afro-Asian monsoon region. Our analysis suggests that on millennial timescales with varying orbital forcing, the monsoons do not behave as a tightly connected global system. According to the models, the Indian and North African monsoons are coupled, showing similar rainfall trend and moderate correlation in rainfall variability in all models. The East Asian monsoon changes independently during the Holocene. The dissimilarities in the seasonality of the monsoon sub-systems lead to a stronger response of the North African and Indian monsoon systems to the Holocene insolation forcing than of the East Asian monsoon and affect the seasonal distribution of Holocene rainfall variations. Within the Indian and North African monsoon domain, precipitation solely changes during the summer months, showing a decreasing Holocene precipitation trend. In the East Asian monsoon region, the precipitation signal is determined by an increasing precipitation trend during spring and a decreasing precipitation change during summer, partly balancing each other. A synthesis of reconstructions and the model results do not reveal an impact of the different seasonality on the timing of the Holocene rainfall optimum in the different sub-monsoon systems. They rather indicate locally inhomogeneous rainfall changes and show, that single palaeo-records should not be used to characterise the rainfall change and monsoon evolution for entire monsoon sub-systems.

An experiment on the parameter uncertainty of hydrological models with different levels of complexity in a climate change context

La possibilité d’estimer l’impact du changement climatique en cours sur le comportement hydrologique des hydro-systèmes est une nécessité pour anticiper les adaptations inévitables et nécessaires que doivent envisager nos sociétés. Dans ce contexte, ce projet doctoral présente une étude sur l’évaluation de la sensibilité des projections hydrologiques futures à : (i) La non-robustesse de l’identification des paramètres des modèles hydrologiques, (ii) l’utilisation de plusieurs jeux de paramètres équifinaux et (iii) l’utilisation de différentes structures de modèles hydrologiques. Pour quantifier l’impact de la première source d’incertitude sur les sorties des modèles, quatre sous-périodes climatiquement contrastées sont tout d’abord identifiées au sein des chroniques observées. Les modèles sont calés sur chacune de ces quatre périodes et les sorties engendrées sont analysées en calage et en validation en suivant les quatre configurations du Different Splitsample Tests (Klemeš, 1986;Wilby, 2005; Seiller et al. (2012);Refsgaard et al. (2014)). Afin d’étudier la seconde source d’incertitude liée à la structure du modèle, l’équifinalité des jeux de paramètres est ensuite prise en compte en considérant pour chaque type de calage les sorties associées à des jeux de paramètres équifinaux. Enfin, pour évaluer la troisième source d’incertitude, cinq modèles hydrologiques de différents niveaux de complexité sont appliqués (GR4J, MORDOR, HSAMI, SWAT et HYDROTEL) sur le bassin versant québécois de la rivière Au Saumon. Les trois sources d’incertitude sont évaluées à la fois dans conditions climatiques observées passées et dans les conditions climatiques futures. Les résultats montrent que, en tenant compte de la méthode d’évaluation suivie dans ce doctorat, l’utilisation de différents niveaux de complexité des modèles hydrologiques est la principale source de variabilité dans les projections de débits dans des conditions climatiques futures. Ceci est suivi par le manque de robustesse de l’identification des paramètres. Les projections hydrologiques générées par un ensemble de jeux de paramètres équifinaux sont proches de celles associées au jeu de paramètres optimal. Par conséquent, plus d’efforts devraient être investis dans l’amélioration de la robustesse des modèles pour les études d’impact sur le changement climatique, notamment en développant les structures des modèles plus appropriés et en proposant des procédures de calage qui augmentent leur robustesse. Ces travaux permettent d’apporter une réponse détaillée sur notre capacité à réaliser un diagnostic des impacts des changements climatiques sur les ressources hydriques du bassin Au Saumon et de proposer une démarche méthodologique originale d’analyse pouvant être directement appliquée ou adaptée à d’autres contextes hydro-climatiques.

Mixture of time-dependent growth models with an application to blue swimmer crab length-frequency data

Understanding how aquatic species grow is fundamental in fisheries because stock assessment often relies on growth dependent statistical models. Length-frequency-based methods become important when more applicable data for growth model estimation are either not available or very expensive. In this article, we develop a new framework for growth estimation from length-frequency data using a generalized von Bertalanffy growth model (VBGM) framework that allows for time-dependent covariates to be incorporated. A finite mixture of normal distributions is used to model the length-frequency cohorts of each month with the means constrained to follow a VBGM. The variances of the finite mixture components are constrained to be a function of mean length, reducing the number of parameters and allowing for an estimate of the variance at any length. To optimize the likelihood, we use a minorization–maximization (MM) algorithm with a Nelder–Mead sub-step. This work was motivated by the decline in catches of the blue swimmer crab (BSC) (Portunus armatus) off the east coast of Queensland, Australia. We test the method with a simulation study and then apply it to the BSC fishery data.

Enhancing the usability of numerical models with case-based reasoning

Abstract not available

Household epidemic models with varying infection response

This paper is concerned with SIR (susceptible--infected--removed) household epidemic models in which the infection response may be either mild or severe, with the type of response also affecting the infectiousness of an individual. Two different models are analysed. In the first model, the infection status of an individual is predetermined, perhaps due to partial immunity, and in the second, the infection status of an individual depends on the infection status of its infector and on whether the individual was infected by a within- or between-household contact. The first scenario may be modelled using a multitype household epidemic model, and the second scenario by a model we denote by the infector-dependent-severity household epidemic model. Large population results of the two models are derived, with the focus being on the distribution of the total numbers of mild and severe cases in a typical household, of any given size, in the event that the epidemic becomes established. The aim of the paper is to investigate whether it is possible to determine which of the two underlying explanations is causing the varying response when given final size household outbreak data containing mild and severe cases. We conduct numerical studies which show that, given data on sufficiently many households, it is generally possible to discriminate between the two models by comparing the Kullback-Leibler divergence for the two fitted models to these data.

Estimating dynamic models with aggregate shocks and an application to mortgage default in Colombia

We estimate a dynamic model of mortgage default for a cohort of Colombian debtors between 1997 and 2004. We use the estimated model to study the effects on default of a class of policies that affected the evolution of mortgage balances in Colombia during the 1990's. We propose a framework for estimating dynamic behavioral models accounting for the presence of unobserved state variables that are correlated across individuals and across time periods. We extend the standard literature on the structural estimation of dynamic models by incorporating an unobserved common correlated shock that affects all individuals' static payoffs and the dynamic continuation payoffs associated with different decisions. Given a standard parametric specification the dynamic problem, we show that the aggregate shocks are identified from the variation in the observed aggregate behavior. The shocks and their transition are separately identified, provided there is enough cross-sectionavl ariation of the observeds tates.

Nature of the spin-glass phase in dense packings of Ising dipoles with random anisotropy axes

By Monte Carlo simulations, we study the character of the spinglass (SG) phase in dense disordered packings of magnetic nanoparticles (NPs). We focus on NPs which have large uniaxial anisotropies and can be well represented as Ising dipoles. Dipoles are placed on SC lattices and point along randomly oriented axes. From the behaviour of a SG correlation length we determine the transition temperature Tc between the paramagnetic and a SG phase. For temperatures well below Tc we find distributions of the SG overlap parameter q that are strongly sample-dependent and exhibit several spikes. We find that the average width of spikes, and the fraction of samples with spikes higher than a certain threshold does not vary appreciably with the system sizes studied. We compare these results with the ones found previously for 3D site-diluted systems of parallel Ising dipoles and with the behaviour of the Sherrington-Kirkpatrick model.

Constrained fuzzy power flow models with correlation between nodal injections

This paper extends the symmetric/constrained fuzzy powerflow models by including the potential correlations between nodal injections. Therefore, the extension of the model allows the specification of fuzzy generation and load values and of potential correlations between nodal injections. The enhanced version of the symmetric/constrained fuzzy powerflow model is applied to the 30-bus IEEE test system. The results prove the importance of the inclusion of data correlations in the analysis of transmission system adequacy.

Diaphragm muscle adaptation to sustained hypoxia: lessons from animal models with relevance to high altitude and chronic respiratory diseases

The diaphragm is the primary inspiratory pump muscle of breathing. Notwithstanding its critical role in pulmonary ventilation, the diaphragm like other striated muscles is malleable in response to physiological and pathophysiological stressors, with potential implications for the maintenance of respiratory homeostasis. This review considers hypoxic adaptation of the diaphragm muscle, with a focus on functional, structural, and metabolic remodeling relevant to conditions such as high altitude and chronic respiratory disease. On the basis of emerging data in animal models, we posit that hypoxia is a significant driver of respiratory muscle plasticity, with evidence suggestive of both compensatory and deleterious adaptations in conditions of sustained exposure to low oxygen. Cellular strategies driving diaphragm remodeling during exposure to sustained hypoxia appear to confer hypoxic tolerance at the expense of peak force-generating capacity, a key functional parameter that correlates with patient morbidity and mortality. Changes include, but are not limited to: redox-dependent activation of hypoxia-inducible factor (HIF) and MAP kinases; time-dependent carbonylation of key metabolic and functional proteins; decreased mitochondrial respiration; activation of atrophic signaling and increased proteolysis; and altered functional performance. Diaphragm muscle weakness may be a signature effect of sustained hypoxic exposure. We discuss the putative role of reactive oxygen species as mediators of both advantageous and disadvantageous adaptations of diaphragm muscle to sustained hypoxia, and the role of antioxidants in mitigating adverse effects of chronic hypoxic stress on respiratory muscle function.

Disagreements among cohabiting and married couples in 22 European countries

Background: Cross-national research suggests that married people have higher levels of well-being than cohabiting people. However, relationship quality has both positive and negative dimensions. Researchers have paid little attention to disagreements within cohabiting and married couples. Objective: This study aims to improve our understanding of the meaning of cohabitation by examining disagreements within marital and cohabiting relationships. We examine variations in couples' disagreements about housework, paid work and money by country and gender. Methods: The data come from the 2004 European Social Survey. We selected respondents living in a heterosexual couple relationship and aged between 18 and 45. In total, the study makes use of data from 22 European countries and 9,657 people. Given that our dependent variable was dichotomous, we estimated multilevel logit models, with (1) disagree and (0) never disagree. Results: We find that cohabitors had more disagreements about housework, the same disagreements about money, but fewer disagreements about paid work than did married people. These findings could not be explained by socio-economic or demographic measures, nor did we find gender or cross-country differences in the association between union status and conflict. Conclusions: Cohabiting couples have more disagreements about housework but fewer disagreements about paid work than married people. There are no gender or cross-country differences in these associations. The results provide further evidence that the meaning of cohabitation differs from that of marriage, and that this difference remains consistent across nations.

Trade-off between formal and informal care in Spain

The remarkable growth of older population has moved long term care to the front ranks of the social policy agenda. Understanding the factors that determine the type and amount of formal care is important for predicting use in the future and developing long-term policy. In this context we jointly analyze the choice of care (formal, informal, both together or none) as well as the number of hours of care received. Given that the number of hours of care is not independent of the type of care received, we estimate, for the first time in this area of research, a sample selection model with the particularity that the first step is a multinomial logit model. With regard to the debate about complementarity or substitutability between formal and informal care, our results indicate that formal care acts as a reinforcement of the family care in certain cases: for very old care receivers, in those cases in which the individual has multiple disabilities, when many care hours are provided, and in case of mental illness and/or dementia. There exist substantial differences in long term care addressed to younger and older dependent people and dependent women are in risk of becoming more vulnerable to the shortage of informal caregivers in the future. Finally, we have documented that there are great disparities in the availability of public social care across regions.

How well do regional or national Breeding Bird Survey data predict songbird population trends at an intact boreal site?

A study to monitor boreal songbird trends was initiated in 1998 in a relatively undisturbed and remote part of the boreal forest in the Northwest Territories, Canada. Eight years of point count data were collected over the 14 years of the study, 1998-2011. Trends were estimated for 50 bird species using generalized linear mixed-effects models, with random effects to account for temporal (repeat sampling within years) and spatial (stations within stands) autocorrelation and variability associated with multiple observers. We tested whether regional and national Breeding Bird Survey (BBS) trends could, on average, predict trends in our study area. Significant increases in our study area outnumbered decreases by 12 species to 6, an opposite pattern compared to Alberta (6 versus 15, respectively) and Canada (9 versus 20). Twenty-two species with relatively precise trend estimates (precision to detect > 30% decline in 10 years; observed SE ≤ 3.7%/year) showed nonsignificant trends, similar to Alberta (24) and Canada (20). Precision-weighted trends for a sample of 19 species with both reliable trends at our site and small portions of their range covered by BBS in Canada were, on average, more negative for Alberta (1.34% per year lower) and for Canada (1.15% per year lower) relative to Fort Liard, though 95% credible intervals still contained zero. We suggest that part of the differences could be attributable to local resource pulses (insect outbreak). However, we also suggest that the tendency for BBS route coverage to disproportionately sample more southerly, developed areas in the boreal forest could result in BBS trends that are not representative of range-wide trends for species whose range is centred farther north.

Forecast encompassing tests and probability forecasts

We consider tests of forecast encompassing for probability forecasts, for both quadratic and logarithmic scoring rules. We propose test statistics for the null of forecast encompassing, present the limiting distributions of the test statistics, and investigate the impact of estimating the forecasting models' parameters on these distributions. The small-sample performance is investigated, in terms of small numbers of forecasts and model estimation sample sizes. We show the usefulness of the tests for the evaluation of recession probability forecasts from logit models with different leading indicators as explanatory variables, and for evaluating survey-based probability forecasts.

Estimativas de parâmetros genéticos para características de crescimento em bovinos da raça Canchim utilizando modelos de dimensão finita

Os objetivos neste trabalho foram avaliar diferentes modelos, em relação aos efeitos maternos considerados, para características de crescimento e estimar os parâmetros genéticos para essas características em bovinos da raça Canchim, por meio de análises uni, bi e multicaracterísticas. As características peso ao nascimento, peso ao desmame, pesos padronizados para 12, 18, 24 e 30 meses de idade em machos e fêmeas e peso adulto de fêmeas foram analisadas utilizando-se quatro modelos com os efeitos aleatórios adicionados em sequência. Os efeitos maternos influenciaram os pesos do nascimento aos 2 anos de idade e o peso à desmama foi o mais afetado pelos efeitos maternos. As estimativas de herdabilidade direta obtidas das análises bi e multicaracterísticas foram superiores àquelas obtidas das análises unicaracterísticas. As estimativas de herdabilidade do efeito genético direto obtidas usando análise multicaracterística foram 0,39 para peso ao nascer; 0,31 para peso à desmama; 0,29 para peso aos 12 meses; 0,28 para peso aos 18 meses; 0,26 para peso aos 24 meses; 0,30 para peso aos 30 meses; e 0,38 para peso à idade adulta. As correlações genéticas estimadas entre pesos obtidos em idades jovens com peso à idade adulta foram altas, acima de 0,79. A seleção com base em características de crescimento em qualquer idade pode promover ganhos genéticos moderados no peso corporal de animais da raça Canchim em todas as idades-padrão, inclusive nos pesos ao nascer e à idade adulta das fêmeas. É importante considerar nas análises os pesos prévios à seleção para estimar parâmetros genéticos para pesos após a seleção. A análise multicaracterística é a mais indicada.